Question

Verify this cofunction identity by using the difference identity for cosine. Show your work! cos⁡(π/2-θ)=sinθ

Answer 1

Cos(A-B) = cosAcosB + sinAsinB

cos(π/2 - θ) = cos(π/2)cosθ + sin(π/2)sinθ

π/2 = 90°
cos(π/2) = cos90° = 0.        sin(π/2) = sin90° = 1

cos(π/2 - θ) = cos(π/2)cosθ + sin(π/2)sinθ

                   = 0*cosθ + 1*sinθ  = sinθ

Therefore  cos(π/2 - θ) = sinθ
 
QED