List of top Mathematics Questions on Trigonometric Functions asked in AP EAPCET

If \[ \tan\alpha=-\frac{7}{24}, \qquad \sec\beta=\frac{61}{60} \] and both \(\alpha,\beta\) lie in the same quadrant, then \[ \cos(\alpha+\beta)= \]
The period of the function \[ f(x)=\log(\cos x)+\cot^4\left(\frac{x}{2}\right)+\sin(3x+7) \] is
Evaluate \[ \cos\frac{\pi}{7}\cos\frac{2\pi}{7}\cos\frac{3\pi}{7} \cos\frac{4\pi}{7}\cos\frac{5\pi}{7}\cos\frac{6\pi}{7}. \]
For \(\theta\in\left(0,\frac{\pi}{2}\right)\), if the complete range of \[ (\cot^2\theta-\cos^2\theta)(\tan^2\theta-\sin^2\theta) \] is \((\alpha,\beta]\), then \(\beta-\alpha=\)
The domain of the function $f(x) = \ln\left(\frac{1}{\sqrt{x^2-4x+4}}\right) + \sin^{-1}(x^2-2)$ is
The number of turning points of the curve $f(x) = 2\cos x - \sin 2x$ in the interval $[-\pi, \pi]$ is
If \( \tan \theta = \frac{3}{4} \) and \( \theta \) is acute, find \( \sin 2\theta \):
If \( \tan \theta = \frac{4}{3} \), find the value of \( \sin \theta \) in the first quadrant.
In \( \Delta ABC \), if \( \angle C = 90^\circ \), then \( \left( \frac{I_1 - I_3}{I_1} \right) \left( \frac{I_2 - I_3}{I_2} \right) = \):
In \( \Delta ABC \), \( A, B, C \) are in arithmetic progression and \( a : c = 1 : 2 \). If \( b = 4\sqrt{3} \) cm, then the area of \( \Delta ABC \) (in sq. cm) is:
If \( \alpha, \beta \) are acute angles such that \( \sin \beta = 2 \sin \alpha \) and \( 3 \cos \beta = 2 \cos \alpha \), then \( \sec (\alpha + \beta) \) is:
In \( \Delta ABC \), \( \left( \tan \frac{A}{2} + \tan \frac{B}{2} \right) \tan \frac{C}{2} = \):
If \( \frac{\tan A}{1 - \cot A} + \frac{\cot A}{1 - \tan A} = \):
If \(\int \frac{dx}{1 + \sin x} = \tan \left( \frac{x}{2} - \theta \right) + C\), then \(\theta =\):
If \( f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x} \) for \( x \in \mathbb{R} \), then find \( f(2023) \).
Evaluate: \[ \cos^2 45^\circ+\cos^2 135^\circ+\cos^2 225^\circ+\cos^2 315^\circ= \]
The value of \[ \cos^4 x \] is
Let \(a\) and \(b\) be non-negative real numbers. If \[ \sin x+a\cos x=b, \] then \[ |a\sin x-\cos x|= \] is equal to:
The value of \[ \sqrt{\sin^4x+4\cos^2x} - \sqrt{\cos^4x+4\sin^2x} \] is
The value of \[ \sin22\frac{1}{2}^{\circ} \] is
If \[ \cos\theta-\sin\theta=\sqrt{5}\sin\theta, \] then \[ \cos\theta+4\sin\theta \] is equal to:
All the pairs \((x,y)\) that satisfy the inequality \[ 2^{\sqrt{\sin^2 x-2\sin x+5}}-\frac{1}{4^{\sin y}}\leq 1 \] also satisfy the equation:
If \[ \sin\theta=-\frac{3}{4}, \] then \[ \sin2\theta= \]
If \[ \frac{1}{\sin1^\circ\sin2^\circ} + \frac{1}{\sin2^\circ\sin3^\circ} +\cdots+ \frac{1}{\sin89^\circ\sin90^\circ} = \] then its value is
Which of the following trigonometric values are negative?
\[ \text{I) } \sin(-292^\circ) \] \[ \text{II) } \tan(-193^\circ) \] \[ \text{III) } \cos(-207^\circ) \] \[ \text{IV) } \cot(-222^\circ) \]