Question

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

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

Answer 1

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

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