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

Solution :

Draw a right angled triangle ABC right angled at B.

Let \(\angle\) A = \(\theta\),  then \(\angle\) C = 90 – \(\theta\)

sin A = \(sin\theta\) = \(BC\over AC\)                     ……..(1)

cos C = \(cos(90 – \theta)\) = \(BC\over AC\)             ……..(2)

From (1) and (2), we have

\(cos(90 – \theta)\) = \(sin\theta\)