Sum and Difference Identities Practice

Multiple Choice

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

• $$\tan\ A\ -\ \tan\ B$$  

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

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

• $$\frac{\sin\ A}{\cos\ B}$$  

Multiple Choice

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

• $$\sin\ 75^{o\ }$$  

• $$\sin\ 33^o\cos42^o+\cos33^o\sin42^o$$  

• $$\sin\ 33^o\cos42^o-\cos33^o\sin42^o$$  

• $$\cos33^o\cos42^o+\sin33^o\sin42^o$$  

Multiple Choice

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

• $$\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

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

• $$\sin\ 90^{o\ }$$  

• $$\sin\ 60^{o\ }$$  

• $$\cos\ 90^{o\ }$$  

• $$\cos\ 60^{o\ }$$  

Multiple Choice

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

• $$\tan75^o$$  

• $$\tan\ 15^o$$  

• $$\frac{\sin45^o}{\cos30^o}$$  

• $$\tan90^{o\ }$$  

Multiple Choice

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

(Use SOH CAH TOA to build reference triangle)

• $$-\frac{33}{65}$$  

• $$\frac{33}{65}$$  

• $$\frac{1}{2}$$  

• $$\frac{12}{13}$$  

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

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

• $$\frac{16}{65}$$  

• $$-\frac{16}{65}$$  

• $$\frac{65}{16}$$  

• $$-\frac{65}{16}$$  

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

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

• $$\tan\ x+1$$  

• $$\tan x-1$$  

• $$\frac{\tan\ x+1}{1-\tan x}$$  

• $$\frac{\tan x-1}{1+\tan x}$$