List of top Mathematics Questions on Trigonometry

If \( \tan^{-1}x + \tan^{-1}y = \frac{\pi}{4} \), then what is the value of \(x + y + xy\)?

If \( \sin x \cos x = \frac{1}{4} \), then the general solution is:

If both \( \alpha \) and \( \beta \) lie in \( \left(-\dfrac{\pi}{4},\,0\right] \), \( \sin(\alpha+\beta) = -\dfrac{33}{65} \), and \( \sin\alpha = -\dfrac{3}{5} \), then \( \tan(2\alpha+\beta) \) is

If \[ \alpha=\tan\left(2\sin^{-1}\left(\frac23\right)\right) \quad\text{and}\quad \beta=\sin\left(2\tan^{-1}\left(\frac13\right)\right), \] then the maximum value of \[ \alpha\sin\theta+\beta\cos\theta \] is

\(a_1,a_2,a_3\) are in arithmetic progression in which common difference is \(2\) and the first term is \(2\). If \[ \cos a_1+\cos a_2+\cos a_3 = \frac{\sin\alpha}{\sin\beta}\cos\gamma, \] then \(\alpha+\beta=\)

If \((\alpha,\beta)\subseteq\left(0,\dfrac{\pi}{2}\right)\) is the smallest set containing all the possible solutions of the inequality \[ \sin x+\cos2x>1, \] then \(\alpha+\beta=\)

If in \((0,2\pi)\), \(2\cos x+k=3\sec x\) and \(\cot x=-1\), then the sum of squares of all possible values of \(k\) is

If \[ \tan(60^\circ+\theta)\tan(60^\circ-\theta) = \frac{a\cos^2\theta-b}{a\cos^2\theta-c}, \] then \[ \frac{a+c}{b}= \]

In a triangle \(ABC\), if \(s=\dfrac{15}{2},\; a=3,\; b=5\), then \[ \frac{\sin \dfrac{B}{2}}{\sin \dfrac{A}{2}}= \]

In a triangle \(ABC\), \[ 2\sqrt{r_1r_2+r_2r_3+r_3r_1} = \]

If \( \theta \) is an acute angle, \( x = \sum_{n=0}^{\infty} \cos^{2n} \theta \), \( y = \sum_{n=0}^{\infty} \sin^{2n} \theta \), then \( \frac{1}{x^2} + \frac{1}{y^2} = \)

For \( A = \frac{\pi}{24} \), if \( \frac{\sin 2A + \sin 3A + \sin 4A}{\cos 2A + \cos 3A + \cos 4A} = k \), then \( (k+1)^2 = \)

The sum of all the values of \( \theta \in \left[\frac{\pi}{2}, 2\pi\right] \) satisfying the equation \( \sin^2\theta \tan\theta + \cos^2\theta \cot\theta = \sin 2\theta \) is:

If \[ \sin^{-1}(2x)-2\cos^{-1}\sqrt{1-x^2}=\frac{\pi}{2}, \] then \(\tan^{-1}(2x+1)=\)

\[ \sin9^\circ\sin18^\circ\sin36^\circ\sin54^\circ\sin72^\circ\sin81^\circ \]

If \(\sin 3A = \cos (A - 26^{\circ})\), where 3A is an acute angle, find the value of A.

A pole 6 m high casts a shadow \(2\sqrt{3}\text{ m}\) long on the ground, then the Sun's angle of elevation is :

In the given figure, the height 'h' is:

\((\frac{2}{5}\cos 0^{\circ} - \frac{1}{5}\sin 0^{\circ})\) is equal to :

Given \(\tan A = \frac{4}{3}\), then \(\cos A\) is :

Sec 855$^{\circ}$ =}

In $\triangle ABC$, if $\sin A = \sin^{2} B$ and $2 \cos^{2} A = 3 \cos^{2} B$ then the triangle ABC is

$\frac{\pi}{2} \le \theta \le \frac{3\pi}{4}$ then $\cos^{-1}(\frac{5}{13} \sin \theta + \frac{12}{13} \cos \theta) =$

Which of the following is not the solution of the equation $\sin 5x = 16 \sin^{5} x (n \in Z)?$

The number of solutions of $\sin x = \frac{x}{10}$ is