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← JEE Main 2016 · 9 Apr · Shift 1
MathematicsSingle correct+4 / -1Question 65 of 90

JEE Main 2016 · 9 Apr · Shift 1, Mathematics question 65

The number of distinct real roots of the equation, ∣cos⁡xsin⁡xsin⁡xsin⁡xcos⁡xsin⁡xsin⁡xsin⁡xcos⁡x∣=0\begin{vmatrix}\cos x&\sin x&\sin x\\\sin x&\cos x&\sin x\\\sin x&\sin x&\cos x\end{vmatrix}=0 in the interval [−π4,π4]\left[-\dfrac\pi4,\dfrac\pi4\right] is :

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Answer and worked solution

Official answer: C

The determinant is (cos⁡x+2sin⁡x)(cos⁡x−sin⁡x)2(\cos x+2\sin x)(\cos x-\sin x)^2. In [−π4,π4]\left[-\frac\pi4,\frac\pi4\right]: tan⁡x=1\tan x=1 at x=π4x=\frac\pi4, and tan⁡x=−12\tan x=-\frac12 at one point. That is 2 roots.

Topics:Trigonometric equationsDeterminants and properties
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