List of top Mathematics Questions on Trigonometry asked in NIMCET

If \( n_1 \) and \( n_2 \) are the number of real valued solutions of \( x = |\sin^{-1} x| \) \(\text{and}\) \( x = \sin(x) \text{ respectively, then the value of} \, n_2 - n_1 \text{ is:}\)

A line segment AB of length 10 meters is passing through the foot of the perpendicular of a pillar, which is standing at right angle to the ground. The tip of the pillar subtends angles \( \tan^{-1}(3) \) and \( \tan^{-1}(2) \) at A and B respectively. Which of the following choices represents the height of the pillar?
If \( \csc\theta - \cot\theta = 2 \), then the value of \( \csc\theta \) is
The correct expression for \( \cos^{-1}(-x) \) is
The solutions of the equation \( 4\cos^2x + 6\sin^2x = 5 \) are
The value of \( \cot(\csc^{-1}\frac{5}{3} + \tan^{-1}\frac{2}{3}) \) is
If \( \cos^{-1}\frac{x}{2} + \cos^{-1}\frac{y}{3} = \phi \), then \( 9x^2 - 12xy\cos\phi + 4y^2 \) is equal to
If the angle of elevation of the top of a hill from each of the vertices A, B and C of a horizontal triangle is \( \alpha \), then the height of the hill is
Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of the tower are 30\(^{\circ}\), 45\(^{\circ}\) and 60\(^{\circ}\) respectively. The ratio of AB and BC is
Solutions of the equation \( \tan^{-1}\sqrt{x^2+x} + \sin^{-1}\sqrt{x^2+x+1} = \frac{\pi}{2} \) are
In a triangle ABC, if the tangent of half the difference of two angles is equal to one third of the tangent of half the sum of the angles, then the ratio of the sides opposite to the angles is