List of top Mathematics Questions on Trigonometric Equations

The sum of all the values of \(\theta\in(0,2\pi)\) satisfying the equation \[ \sin\theta+3\cos2\theta+\sin3\theta = \cos\theta+3\sin2\theta+\cos3\theta \] is

If \(\sin\theta\neq 0\) and \[ \frac{1}{2}\sin\theta,\quad \cos\theta,\quad \cot\theta \] are in geometric progression, then the number of values of \(\theta\) lying in the interval \((-2\pi,2\pi)\) is

If $\cot x=\dfrac{5}{12}$ for some $x\in\left(\pi,\dfrac{3\pi}{2}\right)$, then \[ \sin 7x\left(\cos\frac{13x}{2}+\sin\frac{13x}{2}\right) +\cos 7x\left(\cos\frac{13x}{2}-\sin\frac{13x}{2}\right) \] is equal to:

Number of solutions of the equation \[ \sin\theta+\sin3\theta+\sin5\theta=0 \] in \([-\pi,\pi]\) is

Number of solutions of equation \[ 3^{2\sin^2x}+3^{2\cos^2x}=6 \] lying in interval \[ [-\pi,\pi] \] is

If $\alpha$ and $\beta$ are acute angles such that $\alpha + \beta$ and $\alpha - \beta$ satisfy the equation $\tan^2 \theta - 4\tan \theta + 1 = 0$, then $\alpha$ and $\beta$ are respectively

Find the general solution for \(x\) if \( \cos 4x = \cos 3x \).

Let \( \cos(\alpha + \beta) = -\dfrac{1}{10} \) and \( \sin(\alpha - \beta) = \dfrac{3}{8} \), where \( 0<\alpha<\dfrac{\pi}{3} \) and \( 0<\beta<\dfrac{\pi}{4} \).
If \[ \tan 2\alpha = \frac{3(1 - r\sqrt{5})}{\sqrt{11}(s + \sqrt{5})}, \quad r, s \in \mathbb{N}, \] then the value of \( r + s \) is ______________.

Number of solutions of the equation \[ \sqrt{3} \cos 2\theta + 8 \cos \theta + 3\sqrt{3} = 0 \] in \( \theta \in \left[ -3\pi, 2\pi \right] \):

The number of elements in the set $\{x\in[0,180^\circ]: \tan(x+100^\circ)=\tan(x+50^\circ)\tan x\tan(x-50^\circ)\}$ is

Find the number of solutions of the equation \[ \tan(x+100^\circ)=\tan(x+50^\circ)\tan(x-50^\circ) \] where $x\in(0,\pi)$.

The value of \[ \frac{\sqrt{3}\,\cosec 20^\circ-\sec 20^\circ}{\cos 20^\circ \cos 40^\circ \cos 60^\circ \cos 80^\circ} \] is:

Find the number of solutions of the equation \[ \tan(x+100^\circ)=\tan(x+50^\circ)\tan(x-50^\circ) \] where $x\in(0,\pi)$.

The common principal solution of the equations $\sin \theta = -1/2$ and $\tan \theta = 1/\sqrt{3}$ is \dots}

If $\tan(\pi \cos \theta) = \cot(\pi \sin \theta)$, then $\sin\left(\frac{\pi}{4} + \theta\right) = $ ______.

If $0\le x\le\pi$ and $81^{\sin^{2}x}+81^{\cos^{2}x}=30$ Then $x$ takes the value}

If the difference between the maximum and minimum values of the objective function \(z = 7x - 8y\), subject to the constraints \(x + y \le 20, y \ge 5, x, y \ge 0\) is \(5k + 200\), then the value of k is

If the tangent and the normal at the point \((\sqrt{3}, 1)\) to the circle \(x^2 + y^2 = 4\), and the X-axis form a triangle, then the area (in sq.units) of this triangle is

If $ \cos^{-1}(x) - \sin^{-1}(x) = \frac{\pi}{6} $, then find } $ x $.

Given $ y = \sec(\tan^{-1}(x)) $, find $ \frac{dy}{dx} $ at $ x = \sqrt{3} $.

If $ \tan\left( \alpha - \frac{\pi}{12} \right) = \frac{1}{\sqrt{3}} $, find $ \alpha $.

Principal Solution of $ (5 \sin \theta)(2 \cos \theta + 1) = 0 $

Which of the following expressions represents the Principal Solution