List of top Mathematics Questions on Trigonometric Functions

If \[ \tan\alpha=-\frac{7}{24}, \qquad \sec\beta=\frac{61}{60} \] and both \(\alpha,\beta\) lie in the same quadrant, then \[ \cos(\alpha+\beta)= \]

The period of the function \[ f(x)=\log(\cos x)+\cot^4\left(\frac{x}{2}\right)+\sin(3x+7) \] is

Evaluate \[ \cos\frac{\pi}{7}\cos\frac{2\pi}{7}\cos\frac{3\pi}{7} \cos\frac{4\pi}{7}\cos\frac{5\pi}{7}\cos\frac{6\pi}{7}. \]

For \(\theta\in\left(0,\frac{\pi}{2}\right)\), if the complete range of \[ (\cot^2\theta-\cos^2\theta)(\tan^2\theta-\sin^2\theta) \] is \((\alpha,\beta]\), then \(\beta-\alpha=\)

If $\tan \alpha = \frac{1}{2}$, then the value of $\tan^2(2\alpha) \sec^2(2\alpha)$ is equal to

The value of \[ \tan\!\left(\tan^{-1}(3)+\tan^{-1}(7)\right) \] is equal to:

Let \(f(x)=2\sqrt{\,2\sin x+2\sqrt{2}\cos x\,},\; x\in\mathbb{R}\). Then the value of \(f\!\left(\frac{\pi}{12}\right)\) is equal to

If \(\sin \theta = \frac{3}{5}\) and \(\cos \theta < 0\), then the value of \(\tan \theta\) is

If \(\text{cosec } t + \cot t = \frac{5}{2}\), then the value of \(\tan t\) is equal to

If \[ 1+\cos2\theta+\cos4\theta+\cos6\theta=0, \qquad 0\le\theta\le180^\circ, \] then

The maximum value of $\sin(x + \pi/6) + \cos(x + \pi/6)$ is attained at $x =$

\( \tan^{-1} \left[ 2\cos \left( 2\sin^{-1} \frac{1}{2} \right) \right] = \)_____

\( \sin^{-1} \left(\sin \frac{3\pi}{5}\right) =\) _____

If \( \cos^{-1} x = y \), then _____

\( \int_{0}^{\pi} \left(\sin^2 \frac{x}{2} - \cos^2 \frac{x}{2}\right) dx =\) _____

\( \int \frac{dx}{\sqrt{9x - 4x^2}} = \)_____ + C

\( \int \sec^2 x \cdot \csc^2 x \, dx =\) _____ + C

Find the value of \[ \tan\!\left[\left(2\sin^{-1}\frac{2}{\sqrt{13}}\right)-2\cos^{-1}\!\left(\frac{3}{\sqrt{10}}\right)\right] \]

The no. of solution in \(x \in \left(-\frac{1}{2\sqrt{6}}, \frac{1}{2\sqrt{6}}\right)\) of equation \(\tan^{-1}4x + \tan^{-1}6x = \frac{\pi}{6}\) is :

If the value of \(\frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ}\) is \(\frac{\alpha + \beta\sqrt{5}}{\gamma}\) then value of \((\alpha + \beta + \gamma)\) (where \(\alpha, \beta, \gamma \in \mathbb{N}\) and are in lowest form) :

If \[ \frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \frac{\alpha + \sqrt{5}\,\beta}{2}, \] then the value of \((\alpha + \beta)\) is

$\tan(315^{\circ}) \cot(-405^{\circ}) = $ ________.

$\cos 75^{\circ} \cos 45^{\circ} \cos 15^{\circ} = $ ________.