List of top Mathematics Questions on Trigonometry asked in JEE Main

If 15 sin⁴ α + 10 cos⁴ α = 6, for some α ∈ R, then the value of 27 sec⁶ α + 8 cosec⁶ α is equal to :
Let $f: \mathbb{R} \to \mathbb{R}$ be defined as $f(x+y) + f(x-y) = 2f(x)f(y)$, $f(\frac{1}{2}) = -1$. Then, the value of $\sum_{k=1}^{20} \frac{1}{\sin(k) \sin(k+f(k))}$ is equal to :
Let $\alpha = \max_{x \in \mathbb{R}}\{8^{2\sin 3x} \cdot 4^{4\cos 3x}\}$ and $\beta = \min_{x \in \mathbb{R}}\{8^{2\sin 3x} \cdot 4^{4\cos 3x}\}$.
If $8x^2+bx+c=0$ is a quadratic equation whose roots are $\alpha^{1/5}$ and $\beta^{1/5}$, then the value of c-b is equal to :
If $\tan(\frac{\pi}{9})$, x, $\tan(\frac{7\pi}{18})$ are in arithmetic progression and $\tan(\frac{\pi}{9})$, y, $\tan(\frac{5\pi}{18})$ are also in arithmetic progression, then $|x-2y|$ is equal to :

The solutions of the equation : 

A possible value of \( \tan\!\left(\frac{1}{4}\sin^{-1}\!\left(\frac{\sqrt{63}}{8}\right)\right) \) is :