Question

Prove the validity of the statements.
sec Θ csc(90 - Θ) = 1/ cos^2Θ

Answer 1

We know that \(csc =\dfrac{1}{sin}\) hence \(csc (90-\theta)=\dfrac{1}{sin(90-\theta)}\)

Answer 2

Moreover, \(sin (90-\theta)=sin 90 cos \theta - sin \theta cos 90\) but sin90 =1, and cos 90 =0, hence \(sin(90-\theta)= cos \theta\) and then \(csc (90-\theta)= \dfrac{1}{cos\theta}\)

Answer 3

The rest is a peace of cake, you finish it by yourself