Tan 5xtan 3xtan 2x =

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3.Trigonometrical Ratios, Functions and Identities

easy

$\tan 5x\tan 3x\tan 2x = $

A

$\tan 5x - \tan 3x - \tan 2x$

B

$\frac{{\sin 5x - \sin 3x - \sin 2x}}{{\cos 5x - \cos 3x - \cos 2x}}$

C

$0$

D

None of these

Solution

(a) We have $5x = 3x + 2x $

$\Rightarrow \tan 5x = \tan (3x + 2x)$

==> $\tan 5x = \frac{{\tan 3x + \tan 2x}}{{1 – \tan 3x\tan 2x}}$

==>$\tan 5x – \tan 5x\tan 3x\tan 2x = \tan 3x + \tan 2x$

==> $\tan 5x\tan 3x\tan 2x = \tan 5x – \tan 3x – \tan 2x$.

Standard 11

Mathematics

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