List of top Mathematics Questions on Trigonometric Functions

The period of the function \[ f(x)=\log(\cos x)+\cot^4\left(\frac{x}{2}\right)+\sin(3x+7) \] is
If \[ \tan\alpha=-\frac{7}{24}, \qquad \sec\beta=\frac{61}{60} \] and both \(\alpha,\beta\) lie in the same quadrant, then \[ \cos(\alpha+\beta)= \]
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 \(\beta-\alpha=\)
The value of \(cos(\frac{π}{5})\) is ...
\(cos^{-1}(cos\frac{4π}{3})+sin^{-1}(sin\frac{4π}{3}) = \ldots\)
\(sin(3sin^{-1}(\frac{1}{5})) =\)
If the circles \(x^2+y^2 = 16\) and \(x^2+y^2+2ax+4y+4 = 0\) touch each other internally then \(a =\)
If \(cos43^{\circ}+sin43^{\circ} = k^3\), then \(cos2^{\circ} = \ldots\)
In triangle ABC, with usual notations, if \(a = 4,b = 5\) and \(c = 6\), then angle C is equal to...
The value of \(cos(60^{\circ}-A)\cdot cosA\cdot cos(60^{\circ}+A)\) is
If \(P = tan20^{\circ}\), then the value of \(\frac{tan160^{\circ}-tan110^{\circ}}{1+tan160^{\circ}tan110^{\circ}}\) in terms of \(P\), is...
The value of the expression \(tan(x-9π)\) is equal to:
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:

\(\int \frac{1}{(1 - \cos x)}(1 + \sec x) dx = \) 
 

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