Prove that $Sin(90 – \theta)$ = $Cos\theta$.

Solution :

Draw a right angled triangle ABC right angled at B.

Let $\angle$ A = $\theta$,  then $\angle$ C = 90 – $\theta$

cos A = $cos\theta$ = $AB\over AC$                     ……..(1)

sin C = $sin(90 – \theta)$ = $AB\over AC$             ……..(2)

From (1) and (2), we have

$sin(90 – \theta)$ = $cos\theta$