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Question: If \(\sin x = \frac{- 24}{25},\) then the value of \(\tan x\) is...

If sin⁡x=−2425,\sin x = \frac{- 24}{25}, then the value of tan⁡x\tan x is

A

2425\frac{24}{25}

B

−247\frac{- 24}{7}

C

2524\frac{25}{24}

D

None of these

Answer

−247\frac{- 24}{7}

Explanation

Solution

cos⁡x=1−sin⁡2x=1−(−2425)2=725\cos x = \sqrt{1 - \sin^{2}x} = \sqrt{1 - \left( \frac{- 24}{25} \right)^{2}} = \frac{7}{25}

⇒tan⁡x=sin⁡xcos⁡x=−247\Rightarrow \tan x = \frac{\sin x}{\cos x} = \frac{- 24}{7}.