List of top Mathematics Questions on Trigonometry asked in NIMCET

If $ B = \sin^2y + \cos^4y $, then for all real $ y $,

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships as 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is

If $ \cos^2(10^\circ) \cos(20^\circ) \cos(40^\circ) \cos(50^\circ) \cos(70^\circ) = \alpha + \frac{\sqrt{3}}{16} \cos(10^\circ) $, then $ 3\alpha^{-1} $ is equal to:

A tower subtends an angle of $ 30^\circ $ at a point on the same level as the foot of the tower. At a second point $ h $ meters above the first, the depression of the font of the tower is $ 60^\circ $. What is the horizontal distance of the tower from the point?

$ \text{A tower subtends angles a, 2a, and 3a respectively at points A, B, and C, which are lying on a horizontal line through the foot of the tower. Then }$ $ \frac{AB}{BC} $ $\text{ is equal to:}$

The maximum value of $\sin(x) + \sin(x + 1)$ is $k \cos^{\frac{1}{2}}$ Then the value of $k$ is:

The angles of depression of the top and bottom of an 8m tall building from the top of a multi-storied building are 30° and 45°, respectively. What is the height of the multi-storied building and the distance between the two buildings?

An airplane, when 4000m high from the ground, passes vertically above another airplane at an instant when the angles of elevation of the two airplanes from the same point on the ground are 60° and 30°, respectively. Find the vertical distance between the two airplanes:

The value of $ \tan\left(\frac{\pi}{4} + \theta\right) \times \tan\left(\frac{3\pi}{4} + \theta\right) $ is:

If $ f(x) = \cos([\pi^2] \cdot x) + \cos([-\pi^2] \cdot x) $, where $[ \cdot ]$ denotes the greatest integer function, then $ f\left(\frac{\pi}{2}\right) = $

Find the cardinality of the set $ C $ which is defined as $ C = \{ x \mid \sin(4x) = \frac{1}{2} \text{ for } x \in (-9\pi, 3\pi) \} $:

If $ \sin x = \sin y $ and $ \cos x = \cos y $, then the value of $ x - y $ is:

The perimeter of a triangle $ \triangle ABC $ is 6 times the arithmetic mean of the sines of its angles. If the side $ a $ is 1, then the angle $ A $ is:

If \[ \prod_{i=1}^{n} \tan (\alpha_i) = 1 \forall \alpha_i \in \left[0, \frac{\pi}{2}\right] \text{where} i = 1, 2, 3, \dots, n. \] Then the maximum value of \[ \prod_{i=1}^{n} \sin (\alpha_i) \] is

Largest value of $ \cos^2 \theta - 6 \sin \theta \cos \theta + 3 \sin^2 \theta + 2 $

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