If $\sin \theta - \cos \theta = 0$,then the value of $(\sin^4 \theta + \cos^4 \theta)$ is

  • A
    $\frac{1}{2}$
  • B
    $\frac{3}{4}$
  • C
    $1$
  • D
    $\frac{1}{4}$

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Prove that,
$(\sqrt{3}+ 1) (3-\cot 30^{\circ})=\tan ^{3} 60^{\circ}-2 \sin 60^{\circ}$

$2 \sin ^{2} \theta+4 \sec ^{2} \theta+5 \cot ^{2} \theta+2 \cos ^{2} \theta-4 \tan ^{2} \theta-5 \operatorname{cosec}^{2} \theta = \dots$

If $\cos A = \frac{4}{5}$,then the value of $\tan A$ is

$(1+\tan ^{2} \theta)(1-\cos ^{2} \theta) = \dots$

$\frac{\sin 60^{\circ} + \cos 30^{\circ}}{1 + \sin 30^{\circ} + \cos 60^{\circ}} = \dots$

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