Question

How do you verify the identity `sin(90+A)=cosA`?

Answer 1

Expand using the rule `sin(A + B) = sinAcosB + cosAsinB`.

`sin(90 + A) = cosA`

`sin90cosA + cos90sinA = cosA`

We know, by the unit circle, that `sin90˚ = 1` and `cos90˚ = 0`.

`1(cosA) + 0(sinA) = cosA`

`cosA = cosA`

`LHS = RHS`

Identity proved!

Hopefully this helps!