Which of the following is the same as cos ⁡ ( A + B ) \cos\ \left(A+B\right) cos ( A + B )

cos ⁡ A cos ⁡ B − sin ⁡ A sin ⁡ B \cos\ A\ \cos\ B\ -\ \sin\ A\ \sin\ B cos A cos B − sin A sin B

sin ⁡ A cos ⁡ B + cos ⁡ A sin ⁡ B \sin A\cos\ B\ +\ \cos\ A\ \sin\ B sin A cos B + cos A sin B

sin ⁡ A cos ⁡ B − cos ⁡ A sin ⁡ B \sin\ A\ \cos\ B\ -\ \cos\ A\ \sin\ B sin A cos B − cos A sin B

cos ⁡ A cos ⁡ B + sin ⁡ A sin ⁡ B \cos\ A\ \cos\ B\ +\ \sin\ A\ \sin\ B cos A cos B + sin A sin B

Which of the following is equivalent to tan ⁡ ( A − B ) \tan\ \left(A-B\right) tan ( A − B )

tan ⁡ A − tan ⁡ B 1 + tan ⁡ A tan ⁡ B \frac{\tan\ A\ -\tan\ B}{1+\ \tan A\tan B} 1 + tan A tan B tan A − tan B

tan ⁡ A − tan ⁡ B \tan\ A\ -\ \tan\ B tan A − tan B

tan ⁡ A + tan ⁡ B 1 − tan ⁡ A tan ⁡ B \frac{\tan\ A\ +\tan\ B}{1-\ \tan A\tan B} 1 − tan A tan B tan A + tan B

sin ⁡ A cos ⁡ B \frac{\sin\ A}{\cos\ B} cos B sin A

Expand sin ⁡ ( 3 3 o + 4 2 o ) \sin\ \left(33^{o\ }+42^o\right) sin ( 3 3 o + 4 2 o )

sin ⁡ 3 3 o cos ⁡ 4 2 o + cos ⁡ 3 3 o sin ⁡ 4 2 o \sin\ 33^o\cos42^o+\cos33^o\sin42^o sin 3 3 o cos 4 2 o + cos 3 3 o sin 4 2 o

sin ⁡ 7 5 o \sin\ 75^{o\ } sin 7 5 o

sin ⁡ 3 3 o cos ⁡ 4 2 o − cos ⁡ 3 3 o sin ⁡ 4 2 o \sin\ 33^o\cos42^o-\cos33^o\sin42^o sin 3 3 o cos 4 2 o − cos 3 3 o sin 4 2 o

cos ⁡ 3 3 o cos ⁡ 4 2 o + sin ⁡ 3 3 o sin ⁡ 4 2 o \cos33^o\cos42^o+\sin33^o\sin42^o cos 3 3 o cos 4 2 o + sin 3 3 o sin 4 2 o

Expand cos ⁡ ( π 5 + π 6 ) \cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right) cos ( 5 π + 6 π )

cos ⁡ 2 π 11 \cos\ \frac{2\pi}{11} cos 1 1 2 π

cos ⁡ 7 5 o cos ⁡ 1 5 o − sin ⁡ 7 5 o sin ⁡ 1 5 o \cos75^o\cos15^o-\sin75^{o\ }\sin15^o cos 7 5 o cos 1 5 o − sin 7 5 o sin 1 5 o is equivalent to

cos ⁡ 9 0 o \cos\ 90^{o\ } cos 9 0 o

sin ⁡ 9 0 o \sin\ 90^{o\ } sin 9 0 o

sin ⁡ 6 0 o \sin\ 60^{o\ } sin 6 0 o

cos ⁡ 6 0 o \cos\ 60^{o\ } cos 6 0 o

tan ⁡ 4 5 o + tan ⁡ 3 0 o 1 − tan ⁡ 4 5 o tan ⁡ 3 0 o \frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o} 1 − tan 4 5 o tan 3 0 o tan 4 5 o + tan 3 0 o is equivalent to

tan ⁡ 7 5 o \tan75^o tan 7 5 o

tan ⁡ 1 5 o \tan\ 15^o tan 1 5 o

sin ⁡ 4 5 o cos ⁡ 3 0 o \frac{\sin45^o}{\cos30^o} cos 3 0 o sin 4 5 o

tan ⁡ 9 0 o \tan90^{o\ } tan 9 0 o

Use sum or difference angles identity to find the exact value for sin ⁡ ( − 1 5 o ) \sin\ \left(-15^o\right) sin ( − 1 5 o )

2 − 6 4 \frac{\sqrt{2}-\sqrt{6}}{4} 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

6 + 2 4 \frac{\sqrt{6}+\sqrt{2}}{4} 4 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

6 − 2 4 \frac{\sqrt{6}-\sqrt{2}}{4} 4 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 3 2 -\frac{\sqrt{3}}{2} − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Given sin ⁡ x = 3 5 a n d sin ⁡ y = 2 3 , \sin x=\frac{3}{5}and\ \sin y=\frac{2}{3}, sin x = 5 3 a n d sin y = 3 2 , where x a n d y x\ and\ y x a n d y are both in first quadrant. E v a l u a t e sin ⁡ ( x + y ) Evaluate\ \sin\left(x+y\right) E v a l u a t e sin ( x + y )

3 5 + 8 15 \frac{3\sqrt{5}+8}{15} 1 5 3 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 8

4 5 + 6 15 \frac{4\sqrt{5}+6}{15} 1 5 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 6

2 5 + 12 15 \frac{2\sqrt{5}+12}{15} 1 5 2 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 1 2

4 5 + 2 5 \frac{4\sqrt{5}+2}{5} 5 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 2

If sin ⁡ A = 3 5 , sin ⁡ B = 2 3 , \sin A=\frac{3}{5},\sin B=\frac{2}{3}, sin A = 5 3 , sin B = 3 2 , a n d ∠ A a n d ∠ B and\ \angle A\ and\ \angle B a n d ∠ A a n d ∠ B are acute angles, what is the value of cos ⁡ ( A − B ) ? \cos\left(A-B\right)? cos ( A − B ) ?

4 5 + 6 15 \frac{4\sqrt{5}+6}{15} 1 5 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 6

4 5 − 6 15 \frac{4\sqrt{5}-6}{15} 1 5 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 6

4 5 + 2 5 \frac{4\sqrt{5}+2}{5} 5 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 2

If cos ⁡ A = 1 3 \cos A=\frac{1}{3} cos A = 3 1 , then the positive value of tan ⁡ A 2 \tan\ \frac{A}{2} tan 2 A ?

2 2 \frac{\sqrt{2}}{2} 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

3 \sqrt{3} 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

3 3 \frac{\sqrt{3}}{3} 3 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Sum and Difference Identities

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HSF.TF.C.9, HSG.SRT.C.7, HSG.SRT.C.8

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16 questions

Which of the following is the same as cos⁡ (A+B)\cos\ \left(A+B\right)cos (A+B)

Which of the following is equivalent to tan⁡ (A−B)\tan\ \left(A-B\right)tan (A−B)

Expand sin⁡ (33o +42o)\sin\ \left(33^{o\ }+42^o\right)sin (33o +42o)

Expand cos⁡ (π5+π6)\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)cos (5π​+6π​)

cos⁡75ocos⁡15o−sin⁡75o sin⁡15o\cos75^o\cos15^o-\sin75^{o\ }\sin15^ocos75ocos15o−sin75o sin15o is equivalent to

tan⁡45o+tan⁡30o1−tan⁡45otan⁡30o\frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o}1−tan45otan30otan45o+tan30o​ is equivalent to

Use sum or difference angles identity to find the exact value for cos⁡105o\cos105^ocos105o

Use sum or difference angles identity to find the exact value for sin⁡ (−15o)\sin\ \left(-15^o\right)sin (−15o)

Given sin⁡x=35and sin⁡y=23,\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},sinx=53​and siny=32​, where x and yx\ and\ yx and y are both in first quadrant. Evaluate sin⁡(x+y)Evaluate\ \sin\left(x+y\right)Evaluate sin(x+y)

Write the following expression as the sine, cosine, or tangent of an angle.cos(175)cos(55)+sin(175)sin(55)

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Which of the following is the same as $\cos\ \left(A+B\right)$

Which of the following is equivalent to $\tan\ \left(A-B\right)$

Expand $\sin\ \left(33^{o\ }+42^o\right)$

Expand $\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)$

$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$ is equivalent to

$\frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o}$ is equivalent to

Use sum or difference angles identity to find the exact value for $\cos105^o$

Use sum or difference angles identity to find the exact value for $\sin\ \left(-15^o\right)$

Given $\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$ where $x\ and\ y$ are both in first quadrant. $Evaluate\ \sin\left(x+y\right)$

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)