Which sum or difference identity would you use to verify that sin (90° + q) = cos q?
cos (a - b) = cos a cos b + sin a sin b
sin (a + b) = sin a cos b + cos a sin b
sin (a - b) = sin a cos b - cos a sin b
cos (a + b) = cos a cos b - sin a sin b

Solution:

We have to verify which sum or difference identity will prove sin (90° + q) = cos q

Using the formula,

Sin(A + B) = sinA cosB + cosA sinB

Substituting in the above formula, we get

So, sin(90° + q) = sin 90°cos q + cos 90° Sin q

The value of sin 90° = 1

The value of cos 90° = 0

So, sin(90° + q) = (1) cos q + (0) sin q

sin(90° + q) = cos q + 0

sin(90° + q) = cos q

Therefore, the identity used to verify sin(90° + q) = cos q is sin (a + b) = sin a cos b + cos a sin b.

Which sum or difference identity would you use to verify that sin (90° + q) = cos q?

Summary:

The identity used to verify sin(90° + q) = cos q is sin (a + b) = sin a cos b + cos a sin b.