List of top Mathematics Questions on Trigonometric Functions

Find the value of \( \sin 30^\circ + \cos 60^\circ \).
What is \( \tan \left( \frac{1}{2} \left( \tan^{-1} x + \tan^{-1} \frac{1}{x} \right) \right) \)?
\(\int \frac{\cos 2x}{\cos x + \sin x} dx \)
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.
The value of \( \tan 15^\circ \) is:
The range of the function \( f(x) = 7\cos(10x + 4\pi) \) is
Evaluate the integral: \[ \int \frac{\sin \theta \sin 2\theta}{1 - \cos 2\theta} d\theta. \]
If \( 0<x<\frac{1}{2} \) and \( \alpha = \sin^{-1} x + \cos^{-1} \left(\frac{x}{2} +\frac{\sqrt{3} - 3x^2}{2} \right) \), then \( \tan \alpha + \cot \alpha = \):
Given \( \cos B - \sin A = \frac{\sqrt{3}+1}{4\sqrt{2}} \) and \( 2 \cos A \cos B = \frac{1+\sqrt{2}+\sqrt{3}}{2\sqrt{2}} \), calculate \( \cos^2 \frac{4B}{3} - \sin^2 \frac{4A}{5} \):
If the period of the function \[ f(x) = 2\cos(3x+4) - 3\tan(2x-3) + 5\sin(5x) - 7 \] is \( k \), then \( f(x) \) is periodic with fundamental period \( k \). Find \( k \).
If \(\tan A<0\) and \(\tan 2A = -\frac{4}{3}\), then \(\cos 6A\) is:
Given \((\sin \theta - \csc \theta)^2 + (\cos \theta + \sec \theta)^2 = 5\) and \(\theta\) lies in the third quadrant, find \((\sin \theta + \cos \theta)^3\).
The value of \( \sin 22^{\frac{1}{2}} \) is:
The general solution of $ x $ satisfying the equation $ \sqrt{3} \sin x + \cos x = \sqrt{3} $, is given by

For any real number \(x\), the least value of \(4cosx-3sinx+5\) is ?

If $\tan 15^{\circ}+\frac{1}{\tan 75^{\circ}}+\frac{1}{\tan 105^{\circ}}+\tan 195^{\circ}=2 a$, then the value of $\left(a+\frac{1}{a}\right)$ is :
For a triangle $A B C$, the value of $\cos 2 A+\cos 2 B+\cos 2 C$ is least If its inradius is $3$ and incentre is $M$, then which of the following is NOT correct?

The number of solutions of tanx+secx=2cosx, n(0,2π) are?

In \( \Delta ABC \), if \( \angle C = 90^\circ \), then \( \left( \frac{I_1 - I_3}{I_1} \right) \left( \frac{I_2 - I_3}{I_2} \right) = \):
If for logcos x (cot x) - 4log(sin x) cot x = 1, x = sin-1 \((\frac{\alpha+\sqrt{\beta}}{2})\). Find (α + β), given x ∈ \((0,\frac{\pi}{2})\)
The domain of \(f(x)=\frac{log_{x+1}(x-2)}{e^{2logx}-(2x+3)}\), \(x∈R\) is
Let fn = \(\int\limits_0^{\pi/2}\) \(\left(\displaystyle\sum_{k=1}^{n}\,sin^{k-1}x\right)\left(\displaystyle\sum_{k=1}^{n}\,(2k-1)sin^{k-1}x\right)\) cosx dx, n ∈ N. Then f21 – f20 is equal to____.
If \(\frac{1}{6}\)sinθ.cosθ.tanθ are in G.P, then the solution set θ is

In the angle of the shadow of a 30 m long pool is 10√3m, then the angle elevation of the sun is