List of top Mathematics Questions on Trigonometric Identities asked in MHT CET

In $\triangle ABC$, $(b-c)^2 \cos^2 \frac{A}{2} + (b+c)^2 \sin^2 \frac{A}{2} =$
In $\triangle ABC$, if $2a^2 = b^2 + c^2$, then the value of $\frac{\cos 3A}{\cos A} + 2$ is

In a triangle \( ABC \) with usual notations, if \[ \tan \left( \frac{B-C}{2} \right) = x \cot \left( \frac{A}{2} \right), \] then \( x = \, ? \) 

Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]
Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).
If \( \tan^{-1} (\sqrt{\cos \alpha}) - \cot^{-1} (\cos \alpha) = x \), then what is \( \sin \alpha \)?
If \( \tan(\pi \cos x) = \cot(\pi \sin x) \), then what is \( \sin \left( \frac{\pi}{2} + x \right) \)?