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JEE Main 20252 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
2 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2025 · 2 April · Morning Shift · Mathematics · Trigonometric Equations

If θ ∈[-2 π, 2 π] , then the number of solutions of 2 2 ^2 θ+(2- 6...

If θ∈[−2π,2π]\theta \in[-2 \pi, 2 \pi], then the number of solutions of 22cos⁡2θ+(2−6)cos⁡θ−3=02 \sqrt{2} \cos ^2 \theta+(2-\sqrt{6}) \cos \theta-\sqrt{3}=0, is equal to:

Options

  1. A12
  2. B6
  3. C8
  4. D10

Correct answer

C. 8

Step-by-step solution

22cos⁡2θ+2cos⁡θ−6cos⁡θ−3=0(2cos⁡θ−3)(2cos⁡θ+1)=0cos⁡θ=32,−12\begin{aligned} & 2 \sqrt{2} \cos ^2 \theta+2 \cos \theta-\sqrt{6} \cos \theta-\sqrt{3}=0 \\ & (2 \cos \theta-\sqrt{3})(\sqrt{2} \cos \theta+1)=0 \\ & \cos \theta=\frac{\sqrt{3}}{2}, \frac{-1}{\sqrt{2}}\end{aligned}
Number of solution =8=8
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