List of top Mathematics Questions on Trigonometry asked in CBSE CLASS XII

Evaluate the exact numerical value of the given inverse trigonometric expression: $\sin\left[\cos^{-1} \cos\left(\frac{7\pi}{6}\right)\right]$.
For the inverse trigonometric functions, which of the following Principal Value Branch is not correctly defined ?
The principal value of $\sin^{-1} \left( \sin \left( -\frac{10\pi}{3} \right) \right)$ is :
The value of \( \cos \left( \frac{\pi}{6} + \cot^{-1}(-\sqrt{3}) \right) \) is:
Calculate the area of the region bounded by the curve \[ \frac{x^2}{9} + \frac{y^2}{4} = 1 \] and the x-axis using integration.

The given graph illustrates:

Domain of $f(x) = \cos^{-1} x + \sin x$ is:
Evaluate: \[ I = \int_0^{\frac{\pi}{4}} \frac{\sin x \cos x}{\cos^4 x + \sin^4 x} \, dx \]
Find the domain of $\sin^{-1} \sqrt{x - 1}$.
Simplify $\sin^{-1} \left( \frac{x}{\sqrt{1 + x^2}} \right)$.
Find the particular solution of the differential equation: \[ x^2 \frac{dy}{dx} - xy = x^2 \cos^2\left(\frac{y}{2x}\right), \] given that when \(x = 1\), \(y = \frac{\pi}{2}\).
If \( y = \sqrt{\tan\sqrt{x}} \), prove that: \[ \sqrt{x} \frac{dy}{dx} = \frac{1 + y^4}{4y}. \]
If the direction cosines of a line are \( \sqrt{3}k, \sqrt{3}k, \sqrt{3}k \), then the value of \( k \) is:
Evaluate: \[ \cot^2 \left\{ \csc^{-1}(3) \right\} + \sin^2 \left\{ \cos^{-1} \left( \frac{1}{3} \right) \right\}. \]
If \(y = (\tan x)^x\), then find \(\frac{dy}{dx}\).
The derivative of \( \sin(x^2) \) w.r.t. \( x \), at \( x = \sqrt{\pi} \), is: