List of top Mathematics Questions on Trigonometry asked in MET

If $3\sin^{-1}\!\left(\dfrac{2x}{1+x^{2}}\right) - 4\cos^{-1}\!\left(\dfrac{1-x^{2}}{1+x^{2}}\right) + 2\tan^{-1}\!\left(\dfrac{2x}{1-x^{2}}\right) = \dfrac{\pi}{3}$, then $x$ equals

If $\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \pi$, then $x + y + z$ is

If $\cos^{-1}x + \cos^{-1}y = 2\pi$, then the value of $\sin^{-1}x + \sin^{-1}y$ is equal to

If $\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \pi$, then the value of $x + y + z - xyz$ is

If $4\sin^{-1}x + \cos^{-1}x = \pi$, then $x$ is equal to

In triangle ABC, $(a^2+b^2)\cos A + (b^2+c^2)\cos B + (c^2+a^2)\cos C$ is equal to

If \(0 < \alpha, \beta, \gamma < \frac{\pi}{2}\), such that \(\alpha + \beta + \gamma = \frac{\pi}{2}\) and \(\cot \alpha, \cot \beta, \cot \gamma\) are in AP, then the value of \(\cot \alpha \cot \gamma\) is

In \(\triangle ABC\), if \(a = 4\), \(b = 3\), \(\angle A = 60^\circ\). Then, \(c\) is the root of the equation

In a \(\triangle ABC\), if \(a^2 + b^2 + c^2 = ac + \sqrt{3}ab\), then the triangle is

If \(y = \sqrt{(a-x)(x-b)} - (a-b)\tan^{-1}\sqrt{\frac{a-x}{x-b}}\), then \(\frac{dy}{dx}\) is equal to

If \(\sin^{-1}\left(\frac{x^2 - y^2}{x^2 + y^2}\right) = \log a\), then \(\frac{d^2y}{dx^2}\) equals

The value \(P\) such that the length of subtangent and subnormal is equal for the curve \(y = e^{Px} + Px\) at the point \((0,1)\) is

\(AB\) is a diameter of a circle and \(C\) is any point on the circumference of the circle. Then

The interval for which \(2\tan^{-1}x + \sin^{-1}\frac{2x}{1+x^2}\) is independent of \(x\) is

If \(x, y \in [0, 2\pi]\) then the total number of ordered pairs \((x, y)\) satisfying \(\sin x \cdot \cos y = 1\) is equal to

\(\int x^x \log(ex) dx\) is equal to

Each side of a square subtends an angle of \( 60^\circ \) at the top of a tower \( h \) meters high standing in the center of the square. If \( a \) is the length of each side of the square, then

If \( n \in \mathbb{N} \), then \( |\sin nx| \) is

In \( \triangle ABC \), if \( a = 30, b = 24, c = 18 \), then \( r_3 \) is equal to

In \( \triangle ABC \), \( \frac{b - c}{r_1} + \frac{c - a}{r_2} + \frac{a - b}{r_3} \) is equal to

ABCD is a rectangular field. A vertical lamp post of height 12 m stands at the corner A. If the angle of elevation of its top from B is 60° and from C is 45°, then the area of the field is

The number of values of \( x \) in the interval \( [0, 5\pi] \) satisfying the equation \( 3\sin^2 x - 7\sin x + 2 = 0 \) is

The expression \( \left( 1 + \cos \frac{\pi}{8} \right) \left( 1 + \cos \frac{3\pi}{8} \right) \left( 1 + \cos \frac{5\pi}{8} \right) \left( 1 + \cos \frac{7\pi}{8} \right) \) is equal to

The period of \( \sin(4x + \cos^{4} x) \) is

\( \frac{\cos x}{\cos(x - 2y)} = \lambda \Rightarrow \tan(x - y)\tan y \) is equal to