Prove the following results relating to the tangent of a double angle.

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Prove the following results relating to the tangent of a double angle. (i) Starting with

\sin 2\theta

and

\cos 2\theta

, obtain an expression for

\tan 2\theta

in terms of

\tan\theta

. (ii) Using the result of part (i), verify that

\tan 2\theta\,(1-\tan^{2}\theta)=2\tan\theta

whenever the functions are defined.