Mathematics · 2022
JEE Main · 24 June 2022, Shift 2 · Q13
The number of solutions of the equation cos (x+(π)/3) cos ((π)/3-x)=1/4 cos^2 2 x, x ∈[-3 π, 3 π] is:
The number of solutions of the equation $\displaystyle \cos \left(x+\frac{\pi}{3}\right) \cos \left(\frac{\pi}{3}-x\right)=\frac{1}{4} \cos ^2 2 x$, $\displaystyle x \in[-3 \pi, 3 \pi]$ is:
Official answer
(4)
$\displaystyle 7$
More from Trigonometric Equations
- The number of solutions of the equation 2 θ- cos^2 θ+√2=0 in R is equal to \ \ \ \.2022
- The number of solutions of the equation (4-√3) sin x-2 √3 cos^2 x=-4/(1+√3), x ∈[-2 π, (5 π)/2] is2025
- If the equation cos^4 θ+ sin^4 θ+λ=0 has real solutions for θ, then λ lies in the interval:2020
- The number of elements in the set S={θ ∈[0,2 π]: 3 cos^4 θ-5 cos^2 θ-2 sin^6 θ+2=0} is2023
- The number of solutions, of the equation e^sin x-2 e^- sin x=2, is:2024
- The number of solutions of | cos x|= sin x, such that -4 π ≤ x ≤ 4 π is:2022
- Let S={θ ∈(0,2 π): 7 cos^2 θ-3 sin^2 θ-2 cos^2 2 θ=2}. Then, the sum of roots of all the equations x^2-2( tan^2 θ+ cot^2 θ) x+6 sin^2 θ=0, θ ∈ S, is…2022
- Suppose θ ∈[0, (π)/4] is a solution of 4 cos θ-3 sin θ=1. Then cos θ is equal to:2024
JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.