Question

prove that cos theta×sin(90°-theta)+sin theta×cos(90°-theta)=1

Answer 1

Trigonometry identities:
sin(90°-theta)=cos theta
cos(90°-theta)=sin theta
sin square theta + cos square theta= 1

Answer 2

cosA * sin(90-A) + sinA * cos(90-A)
=cosA * cosA + sinA * sinA
(because sin(90-A) =cosA and cos(90-A)=sinA)
=(cosA)^2 + (sinA)^2
=1
(because (sinA)^2 + (cosA)^2 = 1 trigonometric identity)