Find the value of the trigonometric function $\tan \frac{19 \pi}{3}$.

  • A
    $\sqrt{3}$
  • B
    $-\sqrt{3}$
  • C
    $1/\sqrt{3}$
  • D
    $-1/\sqrt{3}$

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The value of $\frac{\sin 70^{\circ}+\cos 40^{\circ}}{\cos 70^{\circ}+\sin 40^{\circ}}$ is equal to

$\frac{{\cot^2 15^\circ - 1}}{{\cot^2 15^\circ + 1}} = $

The value of $\frac{\sin 55^{\circ} - \cos 55^{\circ}}{\sin 10^{\circ}}$ is

$\frac{\sin \theta}{1-\cot \theta} + \frac{\cos \theta}{1-\tan \theta} = $

Factorize the expression: $2 \cot^2 \theta - \cot \theta - 3$.

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