Question

cos(90+A)=-sinA.
verify that it is an identity.
I know that cos(90-A)=sinA but I am drawing a blank on how to get from there to a verification.

Answer 1

You know that:
cos (90 - A) = sin A
What happens when we trade A for -A in that equation?

Answer 2

cos(90+A)=-sinA
is that all though?

Answer 3

ohh then you could do -sinA=-sinA as a substitution right?

Answer 4

I believe that is all we need.
Since
cos(90 - A) = sin A should be true for any angle A. We can choose B=-A such that
cos(90 - B) = sin B
cos (90 - (-A)) = sin (-A). Simplify, and use the fact that sine is odd. sin(-A) = - sinA
cos(90 + A) = -sin A
And all we had done was change A for -A, so it still works for all values of A.

Answer 5

thank you so much!