Let be any angle for which is defined and let .

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Let

\theta

be any angle for which

\tan\theta

is defined and let

t=\tan\theta

. (i) Express

\sin\theta

solely in terms of

t

. (ii) Express

\cos\theta

solely in terms of

t

. (iii) Using the above results, prove that

1+\tan^2\theta = \dfrac{1}{\cos^2\theta}