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

The correct answer is Option C

Step-by-step explanation:

In this question first we use the sum and difference formula:

cos (a-b) = cos (a) cos (b) + sin (a) sin (b)

Let a = 180 and b = q, then

cos (180-q) = cos (180) cos (q) + sin (180) sin (q)

Now the sin of 180 degree is 0. Since 0 multiplying with anything leaves 0, this makes sin (180) sin (q) = 0

cos (180-q) = cos (180) cos (q)

Now the cos of 180 degree is - 1.

cos (180-q) = - 1 cos (q), or cos (180-q) = - cos (q)