List of top Mathematics Questions on Trigonometry asked in TS EAMCET

\[ \sin9^\circ\sin18^\circ\sin36^\circ\sin54^\circ\sin72^\circ\sin81^\circ \]

The number of values of $\theta$ lying in $[0, 2\pi]$ for which $\sin 3\theta$ attains its maximum when \[ \left|\sin\theta \cdot \sin\left(\frac{\pi}{3} - \theta\right)\cdot \sin\left(\frac{\pi}{3} + \theta\right)\right| \le \frac{1}{8} \] is:

The number of real solutions of the equation \[ \sin^{-1}(2-x) - 2\sin^{-1}x = \pm \frac{\pi}{2} \] is:

If $\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 0$ for $0 \le \theta \le \pi$, then $\theta = $:

If $\theta=\frac{11\pi}{7}$, then \[ \frac{1+\cos 8\theta}{\cot^{2}4\theta} + \frac{1-\cos 8\theta}{\tan^{2}4\theta} = \]

If $\alpha$ and $\beta$ are acute angles and \[ \cos\alpha(1+\tan\alpha\tan\beta)=1, \] then \[ \sin\left(\frac{\alpha-2\beta}{3}\right)= \]

If $A$ and $B$ are the roots of the equation $2x^2-9x-16=0$, then $9\sin^2(A+B)-\cos^2(A+B)=$

If $\sin\theta \sin(60^\circ-\theta)\sin(60^\circ+\theta)=\dfrac18$, then $\cos6\theta=$

If \[ S=\left\{\theta\in\left[\frac{\pi}{2},\frac{3\pi}{2}\right]:\cos^2\theta+\sin\theta\tan\theta=\cos2\theta\right\, \] then \[ \sum_{\theta\in S}(\sin\theta+\cos\theta)= \]

Evaluate: \[ \tan^{-1}\left(\frac12\right) +\tan^{-1}\left(\frac13\right) +\tan^{-1}\left(\frac23\right) +\tan^{-1}\left(\frac15\right) \]

If $2\cos\theta+3\sin\theta=3$ and $\tan\theta$ is defined, then $\tan\theta=$

The number of real solutions of $\tan^{-1}x + \tan^{-1}(2x) = \frac{\pi}{4}$ is

If a, b are real numbers and $\alpha$ is a real root of $x^2+12+3\sin(a+bx)+6x=0$ then the value of $\cos(a+b\alpha)$ for the least positive value of $a+b\alpha$ is

If $\cos\alpha = \frac{l\cos\beta+m}{l+m\cos\beta}$, then $\frac{\tan^2(\alpha/2)}{\tan^2(\beta/2)} =$

If $P = \sin\frac{2\pi}{7} + \sin\frac{4\pi}{7} + \sin\frac{8\pi}{7}$ and $Q = \cos\frac{2\pi}{7} + \cos\frac{4\pi}{7} + \cos\frac{8\pi}{7}$, then the point (P,Q) lies on the circle of radius

If $\tan(\frac{\pi}{4}+\frac{\alpha}{2}) = \tan^3(\frac{\pi}{4}+\frac{\beta}{2})$, then $\frac{3+\sin^2\beta}{1+3\sin^2\beta}=$

If $ x = \log_e 3 $, then $ \tanh(2x) + \operatorname{sech}(2x) = $

$ \sin^{-1}(-\cos 2) + \cos^{-1}(\sin 3) + \tan^{-1}(\cot 5) = $

Number of solutions of the equation $ \tan^2 x + 3\cot^2 x = 2\sec^2 x $ lying in the interval $ [0, 2\pi] $ is

If the extreme values of the function $ f(x) = (2\sqrt{6}+1)\cos x + (2\sqrt{2}-\sqrt{3})\sin x - 6 $ are m and M, then $ \sqrt{|M^2-m^2|} = $

If $ 0 \le A, B \le \frac{\pi}{4} $ and $ \cot A + \cot B + \tan A + \tan B = \cot A \cot B - \tan A \tan B $ then $ \sin(A+B) = $

If $ \cos\theta + \sin\theta = \sqrt{2}\cos\theta $ and $ 0<\theta<\frac{\pi}{2} $, then $ \sec(2\theta) + \tan(2\theta) = $

If $\alpha, \beta$ are the roots of the equation $x^2 + 3x + k = 0$ and $\alpha + 1/\beta$, $\beta + 1/\alpha$ are the roots of the equation $4x^2 + px + 18 = 0$ then k satisfies the equation

If $x \in (-\pi,\pi)$ then the number of solutions of the equation $2 \sin x \sin 3x \sin 5x + \sin 5x \cos 4x = 0$ is

$4 \cos\frac{70}{2}\cos\frac{30}{2} - \sin 50 =$