If tan ,(A + B) = p,,,tan ,(A - B) = q, then value of tan ,2A in terms of p and q is

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3.Trigonometrical Ratios, Functions and Identities

easy

If $\tan \,(A + B) = p,\,\,\tan \,(A - B) = q,$ then the value of $\tan \,2A$ in terms of $p$ and $q$ is

A

$\frac{{p + q}}{{p - q}}$

B

$\frac{{p - q}}{{1 + pq}}$

C

$\frac{{p + q}}{{1 - pq}}$

D

$\frac{{1 + pq}}{{1 - p}}$

Solution

(c) $2A = (A + B) + (A – B)$

$ \Rightarrow $$\tan 2A = \frac{{\tan (A + B) + \tan (A – B)}}{{1 – \tan (A + B)\tan (A – B)}}$

$= \frac{{p + q}}{{1 – pq}}$.

Standard 11

Mathematics

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