Question

Which sum or difference identity would you use to verify that cos (180° - q) = -cos q?

Answer 1

Answer:

c. cos (a -b) = cos a cosb + sin a sin b

Step-by-step explanation:

The given identity is  $\cos (180\degree-q)=-\cos q$

Using the formula: $\cos (a-b)=\cos a\cos b+\sin a \sin b$

We put $a=180\degree$ and $b=q$ to get:

$\cos (180\degree-q)=\cos 180\degree\cos q+\sin 180\degree \sin q$

$\cos (180\degree-q)=-(1)\cos q+(0)\sin q$

$\cos (180\degree-q)=-\cos q+0$

$\cos (180\degree-q)=-\cos q$

The correct answer is C