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

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

Given angle A and B in Quadrant I with sin ⁡ A = 12 13 a n d cos ⁡ B = 3 5 f i n d cos ⁡ ( A + B ) \sin A\ =\frac{12}{13}\ and\ \cos B\ =\frac{3}{5}\ find\ \cos\left(A+B\right) sin A = 1 3 1 2 a n d cos B = 5 3 f i n d cos ( A + B )

− 33 65 -\frac{33}{65} − 6 5 3 3

If sin ⁡ A = 4 5 , tan ⁡ B = 5 12 , \sin A=\frac{4}{5},\tan B=\frac{5}{12}, sin A = 5 4 , tan B = 1 2 5 , and A and B are first quadrant angles, what is the value of sin ⁡ ( A + B ) \sin\left(A+B\right) sin ( A + B ) ?

− 33 65 -\frac{33}{65} − 6 5 3 3

− 63 65 -\frac{63}{65} − 6 5 6 3

Applying Sum and Difference Identities

Authored by Stanley Casie-May

Mathematics

12th Grade

CCSS covered

Used 28+ times

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

$-\frac{2}{3}$

$\frac{4\sqrt{5}-6}{15}$

$\frac{4\sqrt{5}+2}{5}$

$\frac{4\sqrt{5}+6}{15}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

$\frac{3\sqrt{5}+8}{15}$

$\frac{4\sqrt{5}+6}{15}$

$\frac{2\sqrt{5}+12}{15}$

$\frac{4\sqrt{5}+2}{5}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Given $\tan A=\frac{2}{3}and\ \tan B=\frac{1}{2},\$ where $\angle A\ and\ \angle B\ in\ quadrant\ I$ $Evaluate\ \tan\left(A+B\right)$

$\frac{1}{8}$

$\frac{7}{8}$

$\frac{1}{4}$

$\frac{7}{4}$

Tags

CCSS.HSG.SRT.C.8

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Given angle A and B in Quadrant I with $\sin A\ =\frac{12}{13}\ and\ \cos B\ =\frac{3}{5}\ find\ \cos\left(A+B\right)$

$-\frac{33}{65}$

$\frac{33}{65}$

$\frac{1}{2}$

$\frac{12}{13}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\sin A=\ \frac{12}{13\ }\ and\ \cos B=\ \frac{4}{5},\ find\ \cos\left(A+B\right)$ Given angle A and B in Quadrant I with

$\frac{16}{45}$

$\frac{16}{65}$

$\frac{36}{65}$

$\frac{20}{45}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If $\tan A=\frac{2}{3}\ and\ \tan B=\frac{1}{2},$ what is the value of $\tan\left(A+B\right)?$

$\frac{1}{8}$

$\frac{7}{8}$

$\frac{1}{4}$

$\frac{7}{4}$

Tags

CCSS.HSF.TF.C.9

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If $\sin A=\frac{4}{5},\tan B=\frac{5}{12},$ and A and B are first quadrant angles, what is the value of $\sin\left(A+B\right)$ ?

$\frac{63}{65}$

$-\frac{33}{65}$

$\frac{33}{65}$

$-\frac{63}{65}$

Tags

CCSS.HSF.TF.C.9

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Applying Sum and Difference Identities

If sin⁡A=35,sin⁡B=23,\sin A=\frac{3}{5},\sin B=\frac{2}{3},sinA=53​,sinB=32​, and ∠A and ∠Band\ \angle A\ and\ \angle Band ∠A and ∠B are acute angles, what is the value of cos⁡(A−B)?\cos\left(A-B\right)?cos(A−B)?

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)

Given tan⁡A=23and tan⁡B=12, \tan A=\frac{2}{3}and\ \tan B=\frac{1}{2},\ tanA=32​and tanB=21​, where ∠A and ∠B in quadrant I\angle A\ and\ \angle B\ in\ quadrant\ I∠A and ∠B in quadrant I Evaluate tan⁡(A+B)Evaluate\ \tan\left(A+B\right)Evaluate tan(A+B)

Given angle A and B in Quadrant I with sin⁡A =1213 and cos⁡B =35 find cos⁡(A+B)\sin A\ =\frac{12}{13}\ and\ \cos B\ =\frac{3}{5}\ find\ \cos\left(A+B\right)sinA =1312​ and cosB =53​ find cos(A+B)

sin⁡A= 1213 and cos⁡B= 45, find cos⁡(A+B)\sin A=\ \frac{12}{13\ }\ and\ \cos B=\ \frac{4}{5},\ find\ \cos\left(A+B\right)sinA= 13 12​ and cosB= 54​, find cos(A+B) Given angle A and B in Quadrant I with

If tan⁡A=23 and tan⁡B=12,\tan A=\frac{2}{3}\ and\ \tan B=\frac{1}{2},tanA=32​ and tanB=21​, what is the value of tan⁡(A+B)?\tan\left(A+B\right)?tan(A+B)?

If sin⁡A=45,tan⁡B=512,\sin A=\frac{4}{5},\tan B=\frac{5}{12},sinA=54​,tanB=125​, and A and B are first quadrant angles, what is the value of sin⁡(A+B)\sin\left(A+B\right)sin(A+B) ?

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Given angle A and B in Quadrant I with $\sin A\ =\frac{12}{13}\ and\ \cos B\ =\frac{3}{5}\ find\ \cos\left(A+B\right)$

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