Prove that \(Cot(90 – \theta)\) = \(Tan\theta\).

Solution :

Draw a right angled triangle ABC right angled at B.

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

tan A = \(tan\theta\) = \(BC\over AB\)                     ……..(1)

cot C = \(cot(90 – \theta)\) = \(BC\over AB\)             ……..(2)

From (1) and (2), we have

\(cot(90 – \theta)\) = \(tan\theta\)