Using cos2θ=2cos2θ−1:
23cos2θ+8cosθ+23=0⇒3cos2θ+4cosθ+3=0.
cosθ=23−4±2, giving cosθ=−31 or cosθ=−3 (rejected).
Let α=cos−1(−1/3)≈2.186 rad. General solution: θ=2nπ±α.
In [−3π,2π]: θ=α,−α,2π−α,−2π+α,−2π−α.
Total =5 solutions.
Number of solutions of 3cos2θ+8cosθ+33=0,θ∈[−3π,2π] is:
Held on 23 Jan 2026 · Verified 6 Jul 2026.
0
5
3
4
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
If $\cot x=\frac{5}{12}$ for some $x \in\left(\pi, \frac{3 \pi}{2}\right)$, then $\sin 7 x\left(\cos \frac{13 x}{2}+\sin \frac{13 x}{2}\right)+\cos 7 x\left(\cos \frac{13 x}{2}-\sin \frac{13 x}{2}\right)$ is equal to
The value of sin²30° + cos²30° is:
Considering the principal values of inverse trigonometric functions, the value of the expression $\tan \left(2 \sin ^{-1}\left(\frac{2}{\sqrt{13}}\right)-2 \cos ^{-1}\left(\frac{3}{\sqrt{10}}\right)\right)$ is equal to :
The number of solutions of 2sin²x + sin²2x = 2 in [0, 2π] is:
The value of $\frac{\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}}{\cos 20^{\circ} \cos 40^{\circ} \cos 60^{\circ} \cos 80^{\circ}}$ is equal to
Work through every JEE Main Trigonometry PYQ, year by year.