List of top Mathematics Questions on Trigonometry asked in AP EAMCET

In \( \triangle ABC \), if \( A, B, C \) are in arithmetic progression, \( \Delta = \frac{\sqrt{3}}{2} \) and \( r_1 r_2 = r_3 r \), then \( R \) is:
If \[ \cos \alpha + 4 \cos \beta + 9 \cos \gamma = 0 \quad \text{and} \quad \sin \alpha + 4 \sin \beta + 9 \sin \gamma = 0, \] then \[ 81 \cos (2\gamma - 2\alpha) - 16 \cos (2\beta - 2\alpha) = ? \]
tan 9$^\circ$ - tan 27$^\circ$ - tan 63$^\circ$ + tan 81$^\circ$ =
The range of the real valued function \( f(x) = \frac{15}{3 \sin x + 4 \cos x + 10} \) is:
All values of \( (8i)^{\frac{1}{3}} \) are:
Evaluate the sum: \[ \tan^2 \frac{\pi}{16} + \tan^2 \frac{2\pi}{16} + \tan^2 \frac{3\pi}{16} + \tan^2 \frac{4\pi}{16} + \tan^2 \frac{5\pi}{16} + \tan^2 \frac{6\pi}{16} + \tan^2 \frac{7\pi}{16} \]
cos 6° sin 24° cos 72° =
Evaluate the sum: \[ \sin^2 18^\circ + \sin^2 24^\circ + \sin^2 36^\circ + \sin^2 42^\circ + \sin^2 78^\circ + \sin^2 90^\circ + \sin^2 96^\circ + \sin^2 102^\circ + \sin^2 138^\circ + \sin^2 162^\circ. \]
In \( \triangle ABC \), prove the identity: $$ a^2 \sin 2B + b^2 \sin 2A = $$ 
In \( \triangle ABC \), if \( (a+c)^2 = b^2 + 3ca \), then \( \frac{a+c}{2R} \) is:
If A, B, C are the angles of a triangle, then \(\frac{\sin A + \sin B + \sin C}{\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} - 1} =\)
Evaluate the given trigonometric expression: \[ 4 \cos \frac{\pi}{7} \cos \frac{\pi}{5} \cos \frac{2\pi}{7} \cos \frac{2\pi}{5} \cos \frac{4\pi}{7} = \]
In a triangle \( ABC \), if \( A, B, C \) are in arithmetic progression and \[ \cos A + \cos B + \cos C = \frac{1 + \sqrt{2} +\sqrt{3}}{2\sqrt{2}}, \] then \( \tan A \) is:
The general solution of the equation \( \tan x + \tan 2x - \tan 3x = 0 \) is:
The value of \( x \) such that \( \sin \left( 2 \tan^{-1} \frac{3}{4} \right) = \cos \left( 2 \tan^{-1} x \right) \) is:
In \( \triangle ABC \), if \( b + c : c + a : a + b = 7:8:9 \), then the smallest angle (in radians) of that triangle is:
Evaluate $$ \cot \left( \sum_{n=1}^{50} \tan^{-1} \left( \frac{1}{1 + n + n^2} \right) \right).= $$
If \(\sinh x = \dfrac{\sqrt{21}}{2}\) then \(\cosh 2x + \sinh 2x = \)
The values of \( x \) in \( (-\pi, \pi) \) which satisfy the equation \( \cos x + \cos 2x + \cos 3x + \cdots = 4^3 \) are: