List of top Mathematics Questions on Trigonometry asked in TS EAMCET

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

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

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

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

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

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

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

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 \(\alpha, \beta\) 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 $\sin A = -\frac{24}{25}$, $\cos B = \frac{15}{17}$, A does not belong to 4\textsuperscript{th} quadrant and B does not belong to 1\textsuperscript{st} quadrant then $(A + B)$ lies in the quadrant

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

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

If $2 \sin\theta+3 \cos\theta=2$ and $\theta \neq (2n+1)\frac{\pi}{2}$ then $\sin\theta+\cos\theta=$

The number of values of x satisfying the equation $\text{Tan}^{-1}(x+\frac{\sqrt{2}}{x}) + \text{Tan}^{-1}(x-\frac{\sqrt{2}}{x}) = \text{Tan}^{-1}(x)$ is

\( \tan^{-1}\frac{3}{5} + \tan^{-1}\frac{6}{41} + \tan^{-1}\frac{9}{191} = \)

If \( \sin A = -\frac{60}{61} \), \( \cot B = -\frac{40}{9} \) and neither A nor B is in \( 4^{\text{th}} \) quadrant then \( 6\cot A + 4\sec B = \)

If \( 2\tanh^{-1}x = \sinh^{-1}\left(\frac{4}{3}\right) \) then \( \cosh^{-1}\left(\frac{1}{x}\right) = \)

The general solution of the equation \( \sqrt{6 - 5\cos x + 7\sin^2 x} - \cos x = 0 \) also satisfies the equation

If \( A+B+C = 4S \) then \( \sin(2S-A) + \sin(2S-B) + \sin(2S-C) - \sin 2S = \)

The period of the function \( f(x) = \frac{2\sin\left(\frac{\pi x}{3}\right) \cos\left(\frac{2\pi x}{5}\right)}{3\tan\left(\frac{7\pi x}{2}\right) - 5\sec\left(\frac{5\pi x}{3}\right)} \) is

\( \alpha, \beta \) are the roots of the equation \( \sin^2 x + b\sin x + c = 0 \). If \( \alpha + \beta = \frac{\pi}{2} \) then \( b^2 - 1 = \)