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JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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The number of values of ΞΈ\theta in the interval [βˆ’β€‰Ο€,β€…β€Šβ€‰Ο€]\left[ { - \,\pi ,\;\,\pi } \right] satisfying the equation cos⁑  θ+sin⁑  2ΞΈ=0\cos \,\,\theta + \sin \,\,2\theta = 0 is

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Correct option: D
4\mathrm{4}
Option D (4) is correct because there are four values of ΞΈ\theta in the given interval that satisfy the equation.

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The number of solutions of the equation sin⁑  xβ€‰β€‰β€…β€Šcos  3x=sin⁑  3x  cos⁑  5x\sin \,\,x\,\,\;cos\,\,3x = \sin \,\,3x\,\,\cos \,\,5x in [0,β€…β€Šβ€‰Ο€2]\left[ {0,\;\,\frac{\pi }{2}} \right] is The number of ordered pairs (x, y)\left( {x,\,y} \right) where x,  y∈[0,10]x,\,\,y \in \left[ {0,10} \right] satisfying (sin⁑2βˆ’sin⁑  x+12)2sec⁑2y  ⋅  ≀1\left( {\sqrt {{{\sin }^2} - \sin \,\,x + \frac{1}{2}} } \right){2^{{{\sec }^2}y}}\,\, \cdot \,\, \le 1 is Statement I: If slope of the tangent line is zero, then tangent line is perpendicular to the X\mathrm{X}-axis.

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If sin⁑x+cos⁑x=72\sin x+\cos x=\frac{\sqrt{7}}{2}, where x∈[0,Ο€4]x \in\left[0, \frac{\pi}{4}\right], then tan⁑x2\tan \frac{x}{2} is equal to The value of tan⁑π5+2tan⁑2Ο€5+4cot⁑4Ο€5\tan \frac{\pi}{5}+2 \tan \frac{2 \pi}{5}+4 \cot \frac{4 \pi}{5} is If 0<x<Ο€0 < x < \pi and cos⁑x+sin⁑x=12\cos x+\sin x=\frac{1}{2}, then tan⁑x\tan x is equal to
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