List of top Mathematics Questions on Trigonometry asked in KEAM

Solve for \( a \) and \( b \) given the equations: \[ \sin x + \sin y = a, \quad \cos x + \cos y = b, \quad x + y = \frac{2\pi}{3} \]
Given that $ x = \frac{\sin^2 \theta}{\tan \theta - \sec \theta}, \quad y = \frac{\sec \theta + \tan \theta}{\sec^2 \theta}, \quad \text{find} \, \frac{y}{x} $
Evaluate the following expression: $ \frac{\cos 75^\circ - \cos 15^\circ}{\cos 75^\circ + \cos 15^\circ} $
Evaluate the following expression: $ \frac{\cos 75^\circ - \cos 15^\circ}{\cos 75^\circ + \cos 15^\circ} $
Evaluate the expression $ \frac{3 \tan 15^\circ - \tan 3 \times 15^\circ}{1 - 3 \tan^2 15^\circ} $
If \( \cot^{-1} \left( \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \right) \), then find \( \sec^2 \theta \).
If \( \sin \alpha = \frac{12}{13} \), and \( \frac{\pi}{6} \leq \alpha \leq \frac{3\pi}{2} \), find \( \tan \alpha \).
Find \( \tan 15^\circ + \tan 45^\circ \).

The value of \( \cosec x + \cot x \) is

Evaluate \[ \frac{\cosec^2(\theta) - 1}{\cosec^2(\theta)} - \frac{\sec^2(\theta) - 1}{\sec^2(\theta)} \]

If \[ 7 \cos^2 x + 3 \sin^2 x = 6, \] then the value of \( \cos 2x \) is equal to
Let \[ \sum_{k=1}^{15} \sin (t_k) = 0 \quad {and} \quad \sum_{k=1}^{15} \sin (3t_k) = \frac{-24}{5}, \] where \( t_1, t_2, t_3, \dots \) are real numbers. Then the value of the sum \[ \sum_{k=1}^{15} \sin^3 (t_k) \] is equal to
The value of \[ \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{2}{3} \right) + \cot^{-1} \left( \frac{9}{7} \right) \] is equal to
The value of \( \sin \left( 2 \cos^{-1} \left( \frac{5}{12} \right) + \sin^{-1} \left( \frac{5}{12} \right) \right) \) is equal to
If \( \sin t + \cos t = \sqrt{2} \), then \( \tan t + \cot t \) is equal to
The value of \( \tan \left( \cos^{-1} \left( \frac{-24}{25} \right) \right) \) is equal to

Simplify: \( \tan x - \cot x + \csc x \sec x \)

If\( \dfrac{1+sinx}{1-sinx}=\dfrac{(1+siny)^3}{(1-siny)^3}\) for some real values \(x\) and \(y\) ,then \(\dfrac{sinx}{siny}\)=
\(\text{The value of    } cosec20°tan60°-sec20° \text{is }\)
Let \(k\) be a real number such that \(\sin \dfrac{3π}{14} \cos \dfrac{3π}{14} = k \cos \dfrac{π}{14}\).Then the value of \(4k\) is 
Let \(f(x)=αsin^23x\) .If  \(f ′(\dfrac{π}{12})\) = \(−3\),then the value of \(α \) is

In a triangle ABC,if \(cos^{2}A-sin^{2}B+cos^{2}C=0\) ,then the value of \(cosAcosBcosC\) is 

If \(x\) is a real number such that \(tanx+cotx=2\),then \(x=\)?
\(\cos \left( \sin^{-1}(\frac{\sqrt{3}}{200})+\cos^{-1}(\frac{\sqrt{3}}{200}) \right)=\)
If \(\cos\theta=\frac{5}{11}\) and \(\tan\theta\lt0\), then the value of \(\sin\theta\) is equal to