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

Solution :

Draw a right angled triangle ABC right angled at B.

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

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

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

From (1) and (2), we have

\(tan(90 – \theta)\) = \(cot\theta\)