If sin^2x + sinx ,cosx -6cos^2x = 0 and -frac{π}{2} < x < 0 , then value of cos2x , is

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Trigonometrical Equations

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If $sin^2x + sinx \,cosx -6cos^2x = 0$ and $-\frac{\pi}{2} < x < 0$, then the value of $cos2x$, is

A

$-\frac{3}{5}$

B

$\frac{3}{5}$

C

$-\frac{4}{5}$

D

$\frac{4}{5}$

Solution

$\tan ^{2} x+\tan x-6=0 \Rightarrow \tan x=-3$

$\cos 2 x=\frac{1-\tan ^{2} x}{1+\tan ^{2} x}=\frac{1-9}{1+9}=-\frac{4}{5}$

Standard 11

Mathematics

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