List of top Mathematics Questions on Introduction to Trigonometry

Considering only the principal values of the inverse trigonometric functions, evaluate: \[ \cot^{-1}(\cot(-11)) +10\sin\left(2\cos^{-1}\left(\frac1{\sqrt2}\right)\right) +10\sin\left(2\tan^{-1}(2)\right) \]

Assertion (A) : $\tan 2\theta$ is not defined at $\theta = 45^\circ$.
Reason (R) : $\sin 90^\circ \neq \cos 90^\circ$.

Given \(\cot \theta = 3\), the value of \(\cos \theta\) is :

If \(\cos A = \frac{4}{5}\), then the value of \(\tan A\) is :

If \(2 \sin A = 1\), then the value of \(\tan A + \cot A\) is :

If $\cos y = 0$, then what is the value of $\frac{1}{2} \cos \frac{y}{2}$ ?

If $\cos A = \frac{1}{2}$, then the value of $\sin^2 A + 2\cos^2 A$ is :

Given that $\sin \theta = \frac{a}{b}$, then $\cos \theta$ is equal to :

If \(\cos A = \frac{3}{5}\), then the value of \(\tan A\) is :

Assertion (A) : For an acute angle \(\theta\), \(\cos \theta\) is always less than 1.
Reason (R) : In a right-angled triangle, hypotenuse is the longest side and \(\cos \theta = \frac{\text{Base}}{\text{Hypotenuse}}\).

If \(3\tan A = 4 \quad (0^\circ < A < 90^\circ)\), then the value of \(\sin A\) is \dots