5.2 Sum and Difference Formulas

​5.2 Sum and Differences Formulas

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Multiple Choice

Which of the following is equivalent to $$\sin\left(\alpha+\beta\right)$$  ? #1

• $$\sin\alpha\cos\alpha+\sin\beta\cos\beta$$  

• $$\sin\alpha\cos\alpha-\sin\beta\cos\beta$$  

• $$\sin\alpha\cos\beta+\cos\alpha\sin\beta$$  

• $$\sin\alpha\cos\beta-\cos\alpha\sin\beta$$  

Multiple Choice

Given $$\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$$  where  $$x\ and\ y$$  are both in first quadrant.   $$Evaluate\ \sin\left(x+y\right)$$  #12

• $$\frac{3\sqrt{5}+8}{15}$$  

• $$\frac{4\sqrt{5}+6}{15}$$  

• $$\frac{2\sqrt{5}+12}{15}$$  

• $$\frac{4\sqrt{5}+2}{5}$$  

Multiple Choice

Find the exact value of the expression. #20

sin(5π/12)cos(π/4) - cos(5π/12)sin(π/4)

• 1/2

• -1/2

• -√(2)/2

• √(3)/2

Multiple Choice

Use sum or difference angles identity to find the exact value for       $$\sin\ \left(-15^o\right)$$  . #18

• $$\frac{\sqrt{6}+\sqrt{2}}{4}$$  

• $$\frac{\sqrt{6}-\sqrt{2}}{4}$$  

• $$\frac{\sqrt{2}-\sqrt{6}}{4}$$  

• $$-\frac{\sqrt{3}}{2}$$  

Multiple Choice

$$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$$  is equivalent to. #10

• $$\sin\ 90^{o\ }$$  

• $$\sin\ 60^{o\ }$$  

• $$\cos\ 90^{o\ }$$  

• $$\cos\ 60^{o\ }$$  

Multiple Choice

Find the exact value of the expression. $$\sin\left(\frac{5\pi}{12}\right)\cos\left(\frac{\pi}{4}\right)-\cos\left(\frac{5\pi}{12}\right)\sin\left(\frac{\pi}{4}\right)$$  #25

• $$\frac{1}{2}$$  

• $$-\frac{1}{2}$$  

• $$-\frac{\sqrt{2}}{2}$$  

• $$-\frac{\sqrt{3}}{2}$$  

Multiple Choice

Which of the following is the same as $$\cos\ \left(A+B\right)$$  . #7

• $$\sin A\cos\ B\ +\ \cos\ A\ \sin\ B$$  

• $$\sin\ A\ \cos\ B\ -\ \cos\ A\ \sin\ B$$  

• $$\cos\ A\ \cos\ B\ +\ \sin\ A\ \sin\ B$$  

• $$\cos\ A\ \cos\ B\ -\ \sin\ A\ \sin\ B$$  

Multiple Choice

Which of the following is equivalent to $$\cos\left(\alpha-\beta\right)$$  ? #2

• $$\cos\alpha\cos\beta+\sin\alpha\sin\beta$$  

• $$\cos\alpha\cos\beta-\sin\alpha\sin B$$  

• $$\cos\alpha\sin\beta+\sin\alpha\cos\beta$$  

• $$\cos\alpha\sin\beta-\sin\alpha\cos\beta$$  

Multiple Choice

Expand $$\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)$$  . #9

• $$\cos\frac{\pi}{5}\cos\frac{\pi}{6}-\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$$  

• $$\cos\frac{\pi}{5}\cos\frac{\pi}{6}+\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$$  

• $$\cos\ \frac{2\pi}{11}$$  

• $$\cos\frac{\pi}{5}\sin\frac{\pi}{6}-\cos\frac{\pi}{5}\sin\frac{\pi}{6}\$$  

Multiple Choice

If  $$\sin\alpha=\frac{5}{13}$$  and  $$\cos\beta=\frac{4}{5}$$  (both in QI), find  $$\cos\left(\alpha+\beta\right)$$  . #5

• $$\frac{33}{65}$$  

• $$-\frac{33}{65}$$  

• $$\frac{63}{65}$$  

• $$-\frac{63}{65}$$  

Multiple Choice

Which of the following is equivalent to $$\tan\left(\alpha+\beta\right)$$  ? #3

• $$\frac{\tan\alpha+\tan\beta}{1-\tan\alpha\tan\beta}$$  

• $$\frac{\tan\alpha-\tan\beta}{1-\tan\alpha\tan\beta}$$  

• $$\frac{\tan\alpha+\tan\beta}{1+\tan\alpha\tan\beta}$$  

• $$\frac{\tan\alpha-\tan\beta}{1+\tan\alpha\tan\beta}$$  

Multiple Choice

Which of the following is equivalent to $$\tan\ \left(A-B\right)$$  . #8

• $$\tan\ A\ -\ \tan\ B$$  

• $$\frac{\tan\ A\ -\tan\ B}{1+\ \tan A\tan B}$$  

• $$\frac{\tan\ A\ +\tan\ B}{1-\ \tan A\tan B}$$  

• $$\frac{\sin\ A}{\cos\ B}$$  

Multiple Choice

$$\frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o}$$  is equivalent to.. #11

• $$\tan75^o$$  

• $$\tan\ 15^o$$  

• $$\frac{\sin45^o}{\cos30^o}$$  

• $$\tan90^{o\ }$$  

Multiple Choice

Expand and simplify    $$\tan\ \left(x+\frac{\pi}{4}\right)$$  #15

• $$\tan\ x+1$$  

• $$\tan x-1$$  

• $$\frac{\tan\ x+1}{1-\tan x}$$  

• $$\frac{\tan x-1}{1+\tan x}$$