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Question

Question: \[\tan 5x\tan 3x\tan 2x =\]...

tan⁡5xtan⁡3xtan⁡2x=\tan 5x\tan 3x\tan 2x =

A

tan⁡5x−tan⁡3x−tan⁡2x\tan 5x - \tan 3x - \tan 2x

B

sin⁡5x−sin⁡3x−sin⁡2xcos⁡5x−cos⁡3x−cos⁡2x\frac{\sin 5x - \sin 3x - \sin 2x}{\cos 5x - \cos 3x - \cos 2x}

C

0

D

None of these

Answer

tan⁡5x−tan⁡3x−tan⁡2x\tan 5x - \tan 3x - \tan 2x

Explanation

Solution

We have 5x=3x+2x⇒tan⁡5x=tan⁡(3x+2x)5x = 3x + 2x \Rightarrow \tan 5x = \tan(3x + 2x)

⇒ tan⁡5x=tan⁡3x+tan⁡2x1−tan⁡3xtan⁡2x\tan 5x = \frac{\tan 3x + \tan 2x}{1 - \tan 3x\tan 2x}

⇒tan⁡5x−tan⁡5xtan⁡3xtan⁡2x=tan⁡3x+tan⁡2x\tan 5x - \tan 5x\tan 3x\tan 2x = \tan 3x + \tan 2x

⇒ tan⁡5xtan⁡3xtan⁡2x=tan⁡5x−tan⁡3x−tan⁡2x\tan 5x\tan 3x\tan 2x = \tan 5x - \tan 3x - \tan 2x.