If equation 2tan x sin x -2 tan x + cos x = 0 has k solutions in [0,k π] , the

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Trigonometrical Equations

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If the equation $2tan\ x \ sin\ x -2 tan\ x + cos\ x = 0$ has $k$ solutions in $[0,k \pi]$, then number of integral values of $k$ is-

A

$0$

B

$1$

C

$2$

D

$3$

Solution

$2 \tan x \sin x-2 \tan x+\cos ^{3} x=0$

$\frac{2 \sin ^{2} x}{\cos x}-\frac{2 \sin x}{\cos x}+\cos x=0$

$\frac{2 \sin ^{2} x-2 \sin x+\cos ^{2} x}{\cos x}=0$

$\Rightarrow \frac{\sin ^{2} x-2 \sin x+1}{\cos x}=0$

$\Rightarrow \frac{(\sin x-1)^{2}}{\cos x}=0 \Rightarrow \sin x=1$

Standard 11

Mathematics

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