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 cos b + sin a sin b

d.

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

Question

Ashley Watts

Mathematics

8 March, 10:56

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 cos b + sin a sin b

d.

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

+2

Answers (1)

Know the Answer?

Brycen Bowman · Answer 1

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

Step-by-step explanation:

Using 180 as a and q as b:

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

cos 180 = - 1

sin 180 = 0

cos (180 - q) = (-1) cos q + (0) sin q

cos (180 - q) = - cos q

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 bb.cos (a - b) = cos a cos b - sin a sin bc.cos (a - b) = cos a cos b + sin a sin bd.sin (a + b) = sin a cos b + cos a sin b

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 cos b + sin a sin b

d.

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