List of top Mathematics Questions on Trigonometric Equations asked in JEE Main

If $ \theta \in [-2\pi,\ 2\pi] $, then the number of solutions of $$ 2\sqrt{2} \cos^2\theta + (2 - \sqrt{6}) \cos\theta - \sqrt{3} = 0 $$ is:

Let $ A = \left\{ \theta \in [0, 2\pi] : \Re\left( \frac{2 \cos \theta + i \sin \theta}{\cos \theta - 3i \sin \theta} \right) = 0 \right\} $. Then $ \sum_{\theta \in A} \theta^2 $ is equal to:

The number of solutions of the equation $ \cos 2\theta \cos \left( \frac{\theta}{2} \right) + \cos \left( \frac{5\theta}{2} \right) = 2 \cos^3 \left( \frac{5\theta}{2} \right) $ in the interval $\left[ -\frac{\pi}{2}, \frac{\pi}{2} \right ]$ is:

The sum of all values of $ \theta \in [0, 2\pi] $ satisfying $ 2\sin^2\theta = \cos 2\theta $ and $ 2\cos^2\theta = 3\sin\theta $ is:

If for $ \theta \in \left[ -\frac{\pi}{3}, 0 \right] $, the points $ (x, y) = \left( 3 \tan\left( \theta + \frac{\pi}{3} \right), 2 \tan\left( \theta + \frac{\pi}{6} \right) \right) $ lie on $ xy + \alpha x + \beta y + \gamma = 0 $, then $ \alpha^2 + \beta^2 + \gamma^2 $ is equal to:

If $ y = \cos \left( \frac{\pi}{3} + \cos^{-1} \frac{x}{2} \right) $, then $ (x - y)^2 + 3y^2 $ is equal to ________.

If \[ \lim_{x \to 0} \frac{\cos(2x) + a \cos(4x) - b}{x^4} \] is finite, then $ a + b = $ __.

If $ \theta \in \left[ -\frac{7\pi}{6}, \frac{4\pi}{3} \right] $, then the number of solutions of the equation \[ \sqrt{3} \csc^2 \theta - 2 (\sqrt{3} - 1) \csc \theta - 4 = 0 \] is:

The sum of all values of $ \theta \in [0, 2\pi] $ satisfying $ 2\sin^2\theta = \cos 2\theta $ and $ 2\cos^2\theta = 3\sin\theta $ is:

If $\tan A = \frac{1}{\sqrt{x(x^2 + x + 1)}}, \quad \tan B = \frac{\sqrt{x}}{\sqrt{x^2 + x + 1}}$ and $\tan C = \left(x^3 + x^2 + x^{-1}\right)^{\frac{1}{2}}, \quad 0 < A, B, C < \frac{\pi}{2}$,then $ A + B $ is equal to:

If$\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}$is the solution of$ 4cos\theta+ 5sin\theta=1$then the value of $tan\alpha$ is

The number of solutions of \[\sin^2 x + (2 + 2x - x^2) \sin x - 3(x - 1)^2 = 0, \quad \text{where } -\pi \leq x \leq \pi,\] is

The number of solution of equation $e^{sinx} - 2e ^{-sinx} = 2$ is

The number of solution of the equation $4sin^2 x-4cos^3 x+9-4cos x = 0$, $x ∈ [-2\pi, 2\pi]$

Let $f(\theta)=3[sin^4(\frac{3\pi}{2}-\theta)+sin^4(3\pi+θ)]-2(1-sin^22\theta)$ and $S=\{\theta∈[0,\pi]:f'(\theta)=-\frac{\sqrt3}{2}\}$. If $4\beta \sum_{\theta∈S}\theta$, then $f(\beta)$ is equal to

$\lim\limits_{x\rightarrow0}\left(\left(\frac{1-cos^2(3x)}{cos^3(4x)}\right)\left(\frac{sin^3(4x)}{(log_e(2x+1))^5}\right)\right)$is equal to

if f(x)= $\frac{(tan1\degree)x+\log_e(123)}{x\log_e(1234)-(tan1\degree)},x>0$ , then the least value of $f(f(x))+f(f(\frac{4}{x}))$is

f domain of the function \[ f(x) = \log_e \left(\frac{6x^2 + 5x + 1}{2x - 1}\right) + \cos^{-1}\left(\frac{2x^2 - 3x + 4}{3x - 5}\right) \] is $ (\alpha, \beta) \cup (\gamma, \delta) $, then $ 18(\alpha^2 + \beta^2 + \gamma^2 + \delta^2) $ is equal to __________.

Given A, B, C represents angles of a ⃤ AB and cosA + 2 cosB + cosC = 2 and AB = 3 and BC = 7 then cosA – cosC is?

The value of $ 36 \big(4 \cos^2 9^\circ - 1\big) \big(4 \cos^2 27^\circ - 1\big) \big(4 \cos^2 81^\circ - 1\big) \big(4 \cos^2 243^\circ - 1\big) $ is:

Let A = $\left\{ \theta \in (0, 2\pi) : \frac{1 + 2i \sin \theta}{1 - i \sin \theta} \text{ is purely imaginary} \right\}$. Then the sum of the elements in A is.

For x ∈ (–1, 1], the number of solutions of the equation sin^-1x = 2 tan^-1 x is equal to____

The set of all values of $λ$ for which the equation $cos^2⁡2x−2sin^4⁡x−2cos^2⁡x=λ$ has a real solution x, is

The number of solutions of cos4θ – 2cos2θ + 3sin6θ + 1 = 0 in [0, 2π] is

$96\cos\frac{π}{33}\cos \frac{2π}{33}\cos\frac{4π}{33}\cos\frac{8π}{33}\cos\frac{16π}{33}$ is equal to