List of top Mathematics Questions on Trigonometric Identities asked in KEAM

If $\alpha$ and $\beta$ are real constants such that $\alpha - \beta = \frac{\pi}{4}$, then the value of $(\sin \alpha + \sin \beta)^2 + (\cos \alpha + \cos \beta)^2$ is equal to
If $(3 \cos x - 2 \sec x)^2 = 9 \cos^2 x + 4 \tan^2 x + k$, where $k$ is a constant, then the value of $k$ is equal to
The value of the product $\cot 10^\circ \cot 20^\circ \cot 30^\circ \cot 45^\circ \cot 60^\circ \cot 70^\circ \cot 80^\circ$ is equal to
\(\sin 15^\circ \sin 45^\circ \sin 75^\circ =\)
The value of \(\sin(x + \frac{7\pi}{4}) + \sin(x - \frac{7\pi}{4})\) is equal to
$\frac{\sin\frac{\pi}{7}+\sin\frac{2\pi}{7}}{1+\cos\frac{\pi}{7}+\cos\frac{2\pi}{7}} = $ ________.
If $\alpha+\beta+\gamma=2\pi$, then $\tan\frac{\alpha}{2}+\tan\frac{\beta}{2}+\tan\frac{\gamma}{2} = $ ________.
If \(x + z = 2y\) and \(y = \frac{\pi}{4}\), what is \( \tan x \cdot \tan y \cdot \tan z \)?
Find the value of $ \sin 60^\circ - \sin 80^\circ + \sin 100^\circ - \sin 120^\circ $
Solve for $ \alpha $ if: $ \cos^{-1}(2 \sin \alpha) = \frac{47}{12} $
Find the value of $ \cot^{-1}(1) + \cot^{-1}(2) + \cot^{-1}(3) $
Let p,q and r be real numbers such that \(|r|\gt\sqrt{p^2+q^2}\).Then the equation \(p\cos\theta+q\sin\theta=r\) has
If α+β+γ=2π, then the value of \(\cot\frac{\alpha}{2}\cot\frac{\beta}{2}+\cot\frac{\alpha}{2}\cot\frac{\gamma}{2}+\cot\frac{\beta}{2}\cot\frac{\gamma}{2}\) is
If \( \alpha \) and \( \beta \) are two acute angles of a right triangle, then \[ (\sin \alpha + \sin \beta)^2 + (\cos \alpha + \cos \beta)^2 = \] 
If $sin\alpha +sin \beta = \frac{\sqrt6}2$ and $cos \alpha + cos\beta = \frac{\sqrt2}2$ then $coas(\alpha - \beta)$ is equa; to
If \( 0 < x < \pi \), then \( \frac{\sin 8x + 7\sin 6x + 18\sin 4x + 12\sin 2x}{\sin 7x + 6\sin 5x + 12\sin 3x} = \)
If \( \sin \theta + \csc \theta = 2 \), then the value of \( \sin^6 \theta + \csc^6 \theta \) is equal to:
The value of \( \tan(1^\circ) + \tan(89^\circ) \) is equal to:
If \( 0 < x < \pi \), then \( \frac{\sin 8x + 7\sin 6x + 18\sin 4x + 12\sin 2x}{\sin 7x + 6\sin 5x + 12\sin 3x} = \)
The value of \( \tan(1^\circ) + \tan(89^\circ) \) is equal to:
If \( \sin \theta + \csc \theta = 2 \), then the value of \( \sin^6 \theta + \csc^6 \theta \) is equal to:
If \( 0 < x < \pi \), then \( \frac{\sin 8x + 7\sin 6x + 18\sin 4x + 12\sin 2x}{\sin 7x + 6\sin 5x + 12\sin 3x} = \)
The value of \( \tan(1^\circ) + \tan(89^\circ) \) is equal to:
If \( \sin \theta + \csc \theta = 2 \), then the value of \( \sin^6 \theta + \csc^6 \theta \) is equal to:
$ \frac{1}{\cos 80{}^\circ }-\frac{\sqrt{3}}{\sin 80{}^\circ } $ is equal to: