If $A = 30^{\circ}$,then the value of $\cos 2A$ is $\ldots \ldots \ldots . .$

  • A
    $1$
  • B
    $0$
  • C
    $\frac{1}{2}$
  • D
    $\frac{\sqrt{3}}{2}$

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Write 'True' or 'False' and justify your answer.
The value of the expression $(\sin 80^{\circ} - \cos 80^{\circ})$ is negative.

$\frac{\cos ^{2} 40^{\circ}+\cos ^{2} 50^{\circ}}{\sin ^{2} 40^{\circ}+\sin ^{2} 50^{\circ}}=\ldots \ldots \ldots \ldots$

$\cot \theta \cdot \tan \theta = \dots$

If $\cos 9 \alpha = \sin \alpha$ and $9 \alpha < 90^{\circ},$ then the value of $\tan 5 \alpha$ is

$\cos \theta = \frac{b}{\sqrt{a^2 + b^2}}$; where,$0 < \theta < 90^\circ$; then $\sin \theta = \dots$

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