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

\(sin(90 – \theta)\) = \(cos\theta\)