List of top Mathematics Questions on Trigonometry asked in TS EAMCET

If \[ \frac{2x^3+x-3}{x^4-5x^2+4} \] then partial fraction form is

Evaluate \[ 4\sin\frac{\pi}{6}\sin\frac{2\pi}{6}\sin\frac{3\pi}{6}\sin\frac{4\pi}{6}\sin\frac{5\pi}{6} \]

A student found 6 Mathematics books, 5 Physics books and 4 Chemistry books. If he buys at least one book of each subject, total number of ways is

$16 \sin 12^\circ \cos 18^\circ \sin 48^\circ =$

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

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

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 $2 \sin\theta+3 \cos\theta=2$ 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

In a triangle ABC, \( (r_2 + r_3)\sec^2\left(\frac{A}{2}\right) = \)
(Note: Based on the answer key and standard identities, the function is interpreted as \( \sec^2 \)).

In a triangle ABC, if \( r_1=4 \), \( r_2=8 \) and \( r_3=24 \), then \( a:b:c = \)

Consider the following statements:
Assertion (A): When \( x, y, z \) are positive numbers, then \[ \tan^{-1}\left( \sqrt{\frac{x(x+y+z)}{yz}} \right) + \tan^{-1}\left( \sqrt{\frac{y(x+y+z)}{xz}} \right) + \tan^{-1}\left( \sqrt{\frac{z(x+y+z)}{xy}} \right) = \pi \] Reason (R): \( \tan^{-1}a + \tan^{-1}b = \tan^{-1}\left( \frac{a+b}{1-ab} \right) \) if \( a>0 \) and \( b>0 \).