Question

What does sin(pi + theta) + cos(pi/2 - theta) simplify to? sin theta + cos theta 2 cos theta 0 1

Answer 1

Answer:

0

Explanation:

We utilise the following two properties of sines and cosines to simplify our expression.

$\sin(\pi+x)=-\sin(x)$

and

$\cos(\frac{\pi}{2}-x)=\sin(x)$

Substituting the above simplifications into our expression gives

$\sin(\pi+x)+\cos(\frac{\pi}{2}-x)\rightarrow-\sin(x)+\sin(x)=0$

Therefore we conclude that

$\boxed{\sin(\pi+x)+\cos(\frac{\pi}{2}-x)=0.}$