List of top Mathematics Questions on Trigonometric Functions asked in KEAM

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

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

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

$\cos 75^{\circ} \cos 45^{\circ} \cos 15^{\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: $ \sin 75^\circ \times \sin 15^\circ \times \sin 45^\circ $

Evaluate the integral: \[ \int \frac{\sin \theta \sin 2\theta}{1 - \cos 2\theta} d\theta. \]

The value of a(≠0) for which the equation \(\frac{1}{2}(x-2)^2+1=\sin(\frac{a}{x})\) holds is/are

If, \(x∈(0,π)\) satisfies the equation \(6^{1+sinx+sin^2x....}=36\) ,then the value of \(x\) is_____.

Let α and β be such that α+β=π. If \(\cos\alpha=\frac{1}{\sqrt2}\), then the value of cot (β-α) is

Let P(x)=cos²x+sin⁴x,for any x∈R.Then which of the following options is correct for all x?

If x and y are both non-negative and if x+y=π, then the maximum value of 5sinxsiny is equal to

The value of \(\cos^{-1}(\cos(\frac{7\pi}{6}))\) is equal to

If \(\theta \isin(-\pi,0)\ and\ cos\theta=\frac{-12}{13}, then\ \sin(\frac{\theta}{2})=\)

The period of the function \(g(x)=5\cot(\frac{\pi}{3}x+\frac{\pi}{6})+2\) is equal to

The range of the function f(x) = 2sin(3x) +1 is equal to

Let f: R→R be defined by f(x) = cos x. Then

The values of x in the interval $[0,\pi]$ such that $sin 2x = \frac{\sqrt3}2$

$cos^4 \frac{\pi}{12} - sin^4 \frac{\pi}{12}$ is equal to