(i) Express as the quotient of and . (ii) By simplifying the expression obtained in…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

(i) Express

\tan 2\theta

as the quotient of

\sin 2\theta

and

\cos 2\theta

. (ii) By simplifying the expression obtained in part (i), prove that

\tan 2\theta=\dfrac{2\tan \theta}{1-\tan^2\theta}.

(iii) State the values of

\theta

(within

0\le \theta<\pi

) for which the formula in part (ii) is not defined, giving a brief reason in each case.