Verified Solution • 2025–26 Session moderate

QJEEM20Ma601c: JEE Main 2020 Mathematics - Class 11 JEEM20Ma601c Solution: If the equation cos 4 + sin 4 + = 0 has real solutions for ,…

If the equation cos4 θ\theta + sin4 θ\theta + λ\lambda = 0 has real solutions for θ\theta , then λ\lambda lies in the interval :

Multiple Choice Options

  • A [−32,−54]\left[ { - {3 \over 2}, - {5 \over 4}} \right]
  • B (−12,−14]\left( { - {1 \over 2}, - {1 \over 4}} \right]
  • C (−54,−1]\left( { - {5 \over 4}, - 1} \right]
  • D [−1,−12]\left[ { - 1, - {1 \over 2}} \right]

Step-by-Step Verified Solution

cos4 θ\theta + sin4 θ\theta + λ\lambda = 0

⇒\Rightarrow 1 – 2sin2 θ\theta cos2 θ\theta = - λ\lambda

⇒\Rightarrow 1 - 12×4\frac{1}{2} \times 4 sin2 θ\theta cos2 θ\theta = - λ\lambda

⇒\Rightarrow 1 - sin⁡22θ2\frac{\sin^{2} 2\theta }{2} = - λ\lambda

⇒\Rightarrow 2( λ\lambda + 1) = sin2 2 θ\theta

0 ≤\le 2 ( λ\lambda + 1) ≤\le 1

0 ≤\le ( λ\lambda + 1) ≤\le 12\frac{1}{2}

-1 ≤\le λ\lambda ≤\le - 12\frac{1}{2}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring