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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main · Mathematics · Trigonometric Equations

If 2 ^ 2 x+7 x=5 , then permissible value of x is

If 2sin⁡2x+7cos⁡x=52 \sin ^{2} x+7 \cos x=5, then permissible value of cos⁡x\cos x is

Options

  1. A12\frac{1}{2}
  2. B0
  3. C1
  4. D−12-\frac{1}{2}

Correct answer

A. 12\frac{1}{2}

Step-by-step solution

We have 2cos⁡2θ+3cos⁡θ=22cos⁡2θ+4cos⁡θ−cos⁡θ−2=0⇒2cos⁡θ(cos⁡θ+2)−1(cos⁡θ+2)=0(2cos⁡θ−1)(cos⁡θ+2)=0∴cos⁡θ=12,−22 \cos ^{2} \theta+3 \cos \theta=22 \cos ^{2} \theta+4 \cos \theta-\cos \theta-2=0 \Rightarrow 2 \cos \theta(\cos \theta+2)-1(\cos \theta+2)=0(2 \cos \theta-1)(\cos \theta+2)=0\therefore \cos \theta=\frac{1}{2},-2 (Impossible) ⇒cos⁡θ=12\Rightarrow \cos \theta=\frac{1}{2}
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