List of top Mathematics Questions on Some Applications of Trigonometry asked in JEE Main

The number of values of \( x \) satisfying \( \tan^{-1}(4x) + \tan^{-1}(6x) = \frac{\pi}{6} \) and \( x<\left[ \frac{-1}{2\sqrt{6}} , \frac{1}{2\sqrt{6}} \right] \) is:

If \[ \frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \frac{\alpha + \sqrt{5\beta}}{2} \] then the value of \( (\alpha + \beta) \) is:

The value of cosec10° - √3 sec10°

The number of solutions of the equation \( \tan 3x = \cot x \) in \( x \in [0, 2\pi] \) is:

The minimum value of \( (\sin^{-1} x)^2 + (\cos^{-1} x)^2 \) in \( x \in \left[ \frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}} \right] \) is \( \frac{a \pi^2}{b} \), then \( a + b \) is:

If \(4 cos\ θ + 5 sin\ θ = 1\), then all possible values of \(tan\ θ\), is/are
Where, \(θ∈(-\frac \pi2,\frac \pi2)\)

If \(\frac {3cos\ 2x+cos^32x}{cos^6x-sin^6x}=x^3-x^2+6\), then find sum of roots.

Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let \(\frac \pi 8\) and \(θ\) be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then \(tan^2θ\) is equal to

A tower stands at the center of a circular park. $A$ and $B$ are two points on the boundary of the park such that $AB=a$ subtends an angle ${60}^{\circ }$ of at the foot of the tower and the angle of elevation of the top of the tower from $A$ or $B$ is ${30}^{\circ }$. The height of the tower is