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} = $ ________.

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 \( \frac{\sin 8x + 7\sin 6x + 18\sin 4x + 12\sin 2x}{\sin 7x + 6\sin 5x + 12\sin 3x} = \)

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: