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Question: If \(\sin x + \cos x = \frac{1}{5},\) then \(\tan 2x\) is...

If sin⁡x+cos⁡x=15,\sin x + \cos x = \frac{1}{5}, then tan⁡2x\tan 2x is

A

2517\frac{25}{17}

B

725\frac{7}{25}

C

257\frac{25}{7}

D

247\frac{24}{7}

Answer

247\frac{24}{7}

Explanation

Solution

sin⁡x+cos⁡x=15\sin x + \cos x = \frac{1}{5} ⇒ sin⁡2x+cos⁡2x+2sin⁡xcos⁡x=125\sin ^ { 2 } x + \cos ^ { 2 } x + 2 \sin x \cos x = \frac { 1 } { 25 }

sin⁡2x=−2425\sin 2x = - \frac{24}{25} ⇒ cos⁡2x=−725\cos 2x = - \frac{7}{25} ⇒ tan⁡2x=247\tan 2x = \frac{24}{7}.