The values of $x$ in $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $\sin x \cos x = \frac{1}{4}$ are $.......$

  • A
    $\frac{\pi}{6}, \frac{\pi}{12}$
  • B
    $\frac{\pi}{12}, \frac{5 \pi}{12}$
  • C
    $\frac{\pi}{8}, \frac{3 \pi}{8}$
  • D
    $\frac{\pi}{8}, \frac{\pi}{4}$

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$(b)$ $\cos 930^{\circ}$
$(c)$ $\tan 840^{\circ}$
$(d)$ $\cot (-1110^{\circ})$

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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:

The value of $(\sin 210^{\circ})(\sin 585^{\circ})$ is

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