List of top Mathematics Questions on Trigonometric Functions

Evaluate the limit: \[ \lim_{x \to 0} \csc{x} \left( \sqrt{2 \cos^2{x} + 3 \cos{x}} - \sqrt{\cos^2{x} + \sin{x} + 4} \right) \] is equal to:

Let \( M \) and \( m \) respectively be the maximum and the minimum values of \( f(x) = \begin{vmatrix} 1 + \sin^2x & \cos^2x & 4\sin4x \\ \sin^2x & 1 + \cos^2x & 4\sin4x \\ \sin^2x & \cos^2x & 1 + 4\sin4x \end{vmatrix}, \quad x \in \mathbb{R} \)  for \( x \in \mathbb{R} \). Then \( M^4 - m^4 \) is equal to:

If \( \alpha>\beta>\gamma>0 \), then the expression \[ \cot^{-1} \beta + \left( \frac{1 + \beta^2}{\alpha - \beta} \right) + \cot^{-1} \gamma + \left( \frac{1 + \gamma^2}{\beta - \gamma} \right) + \cot^{-1} \alpha + \left( \frac{1 + \alpha^2}{\gamma - \alpha} \right) \] is equal to:

Evaluate: $ \tan^{-1} \left[ 2 \sin \left( 2 \cos^{-1} \frac{\sqrt{3}}{2} \right) \right]$
What is \( \tan \left( \frac{1}{2} \left( \tan^{-1} x + \tan^{-1} \frac{1}{x} \right) \right) \)?
\(\int \frac{\cos 2x}{\cos x + \sin x} dx \)
Solve for \( x \), \[ 2 \tan^{-1} x + \sin^{-1} \left( \frac{2x}{1 + x^2} \right) = 4\sqrt{3} \]

The graph shown below depicts:

Evaluate: \( \sin^{-1} \left( \sin \frac{3\pi}{5} \right) \).
The graph of a trigonometric function is as shown. Which of the following will represent the graph of its inverse?
graph of a trigonometric function
The number of turning points of the curve $f(x) = 2\cos x - \sin 2x$ in the interval $[-\pi, \pi]$ is
The domain of the function $f(x) = \ln\left(\frac{1}{\sqrt{x^2-4x+4}}\right) + \sin^{-1}(x^2-2)$ is
If \( \tan \theta = \frac{3}{4} \) and \( \theta \) is acute, find \( \sin 2\theta \):
If \( \tan \theta = \frac{4}{3} \), find the value of \( \sin \theta \) in the first quadrant.
If \( \tan \theta = 2 \), then the value of \( \sec^2 \theta \) is:
Find the value of \( x \) if \( \sin(2x) = 1 \).
Evaluate the limit \[ \lim_{x \to 0} \frac{\tan \left( -\pi^2 x^2 - x^2 \tan \left( -\pi^2 \right) \right)}{\sin^2 x} \] is:
Let \( f_n(x) = \tan\left(\frac{x}{2}\right)(1+\sec x)(1+\sec 2x)\dotsm(1+\sec 2^{n}x) \), then which of the following is true?
Find the value of: $ \sin 75^\circ \times \sin 15^\circ \times \sin 45^\circ $
Find the value of the following expression: \[ \sin^2(30^\circ) + \cos^2(60^\circ) \]
If \( f(x) = \cos x \), find the following expression: \[ \frac{1}{2} \left[ f(x + y) + f(y - x) - f(x) \cdot f(y) \right] \]
Find the value of \( \tan 45^\circ \).
If \( \sin \theta = \frac{3}{5} \), find the value of \( \cos \theta \).
Find the value of \( \sin 30^\circ + \cos 60^\circ \).
If \( f(\theta) = \frac{\tan(\tan(\theta)) - \tan(\sin(\theta))}{\tan(\theta) - \sin(\theta)} \) is continuous at \( \theta = 0 \), then the value of \( f(\theta) \) at \( \theta = 0 \) is equal to.