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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