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$\sin 120^{\circ} \cos 150^{\circ} - \cos 240^{\circ} \sin 330^{\circ}$ is equal to :

Prove that: $\sin ^{2} \frac{\pi}{6}+\cos ^{2} \frac{\pi}{3}-\tan ^{2} \frac{\pi}{4}=-\frac{1}{2}$

Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length $15\, cm$.

If $\sin \theta = \frac{24}{25}$ and $\theta$ lies in the second quadrant,then $\sec \theta + \tan \theta = $

The expression $\frac{\tan(x - \frac{\pi}{2}) \cdot \cos(\frac{3\pi}{2} + x) - \sin^3(\frac{7\pi}{2} - x)}{\cos(x - \frac{\pi}{2}) \cdot \tan(\frac{3\pi}{2} + x)}$ simplifies to:

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