$\frac{1}{\sin ^{2} \theta}-1 = \ldots \ldots \ldots$

  • A
    $\cos ^{2} \theta$
  • B
    $\cot ^{2} \theta$
  • C
    $\tan ^{2} \theta$
  • D
    $\sec ^{2} \theta$

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State whether the following is 'True' or 'False' and justify your answer:
If $\cos A + \cos^2 A = 1$,then $\sin^2 A + \sin^4 A = 1$.

In $\Delta ABC$,$m \angle C = 90^{\circ}$ and $\cos B = \frac{1}{2}$,then $\operatorname{cosec} A = \ldots$

If $\sin \theta + \cos \theta = \sqrt{3}$,then prove that $\tan \theta + \cot \theta = 1$.

$\sin \theta \cdot \cos (90^\circ - \theta) = \ldots \ldots \ldots$

$\sin^{2} 15^{\circ} + \sin^{2} 75^{\circ} = \dots$

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