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List of top Mathematics Questions on Trigonometry asked in JEE Main

The number of solutions of the equation \[4 \sin^2 x - 4 \cos^3 x + 9 - 4 \cos x = 0, \, x \in [-2\pi, 2\pi]\]is:
A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle are \( m \) and \( n \), respectively, then \( m + n^2 \) is equal to:
The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is
Let \[ S = \{ \sin^2 2\theta : (\sin^4 \theta + \cos^4 \theta)x^2 + (\sin 2\theta)x + (\sin^6 \theta + \cos^6 \theta) = 0 \, \text{has real roots} \}. \] If \( \alpha \) and \( \beta \) are the smallest and largest elements of the set \( S \), respectively, then \[ 3 \big((\alpha - 2)^2 + (\beta - 1)^2 \big) \] equals:
If the value of \[ \frac{3 \cos 36^\circ + 5 \sin 18^\circ}{5 \cos 36^\circ - 3 \sin 18^\circ} = \frac{a\sqrt{5} - b}{c}, \] where \(a, b, c\) are natural numbers and \(\text{gcd}(a, c) = 1\), then \(a + b + c\) is equal to:
If $\sin x = -\frac{3}{5}$, where $\pi<x<\frac{3\pi}{2}$, then $80(\tan^2 x - \cos x)$ is equal to:
Let \[ \left| \cos \theta \cos (60^\circ - \theta) \cos (60^\circ - \theta) \right| \leq \frac{1}{8}, \quad \theta \in [0, 2\pi] \] Then, the sum of all \( \theta \in [0, 2\pi] \), where \( \cos 3\theta \) attains its maximum value, is:
Suppose \( \theta \in \left[ 0, \frac{\pi}{4} \right] \) is a solution of \( 4 \cos \theta - 3 \sin \theta = 1 \). Then \( \cos \theta \) is equal to:
For \( \alpha, \beta, \gamma \neq 0 \). If \( \sin^{-1} \alpha + \sin^{-1} \beta + \sin^{-1} \gamma = \pi \) and \( (\alpha + \beta + \gamma)(\alpha - \gamma + \beta) = 3 \alpha \beta \), then \( \gamma \) is equal to
\[\text{Let } A = \begin{bmatrix} 2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2 \end{bmatrix} \text{ and } P = \begin{bmatrix} 1 & 2 & 0 \\ 5 & 0 & 2 \\ 7 & 1 & 5 \end{bmatrix}.\]The sum of the prime factors of \( |P^{-1}AP - 2I| \) is equal to.
If \( a = \sin^{-1} (\sin(5)) \) and \( b = \cos^{-1} (\cos(5)) \), then \( a^2 + b^2 \) is equal to
The number of solutions of the equation \(e^{\sin x} - 2e^{-\sin x} = 2\) is
Let \( x = \frac{m}{n} \) ( \( m, n \) are co-prime natural numbers) be a solution of the equation \( \cos \left( 2 \sin^{-1} x \right) = \frac{1}{9} \) and let \( \alpha, \beta (\alpha > \beta) \) be the roots of the equation \( mx^2 - nx - m + n = 0 \). Then the point \( (\alpha, \beta) \) lies on the line
For \( \alpha, \beta \in \left( 0, \frac{\pi}{2} \right) \), let \( 3 \sin(\alpha + \beta) = 2 \sin(\alpha - \beta) \) and a real number \( k \) be such that \( \tan \alpha = k \tan \beta \). Then the value of \( k \) is equal to:
Let the set of all \( a \in \mathbb{R} \) such that the equation \(\cos 2x + a \sin x = 2a - 7\) has a solution be \([p, q]\) and \( r = \tan 9^\circ - \tan 27^\circ - \frac{1}{\cot 63^\circ + \tan 81^\circ} \), then \( pqr \) is equal to ______.
If \( 2 \sin^3 x + \sin 2x \cos x + 4 \sin x - 4 = 0 \) has exactly 3 solutions in the interval \( \left[ 0, \frac{n \pi}{2} \right] \), \( n \in \mathbb{N} \), then the roots of the equation \( x^2 + nx + (n - 3) = 0 \) belong to:
The angle of elevation of the top P of a tower from the feet of one person standing due South of the tower is 45° and from the feet of another person standing due west of the tower is 30°. If the height of the tower is 5 meters, then the distance (in meters) between the two persons is equal to

If sin2(10°)sin(20°)sin(40°)sin(50°)sin(70°) 
\(=α−\frac{1}{16}sin⁡(10^∘),\)
 then 16 + α–1 is equal to _______

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is :

Let \(S=\left\{θ∈[0,2π]:8^{2sin^2⁡θ}+8^{2cos^2⁡θ}=16\right\}\) .
Then\(n(S) + \sum_{\theta \in S}\left( \sec\left(\frac{\pi}{4} + 2\theta\right)\cosec\left(\frac{\pi}{4} + 2\theta\right)\right)\)is equal to :

If 
\(cot α=1\) and \(sec β=−\frac{5}{3}\) where \(π<α<\frac{3π}{2} and \frac{π}{2}<β<π\)
, then the value of tan(α + β) and the quadrant in which α + β lies, respectively are :

16 sin(20°) sin(40°) sin(80°) is equal to :

If the sum of solutions of the system of equations 2sin2θ – cos2θ = 0 and 2cos2θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

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