NDA MATHEMATICS QUIZ - 21

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Question 1:

If $\sin (\pi \cos x)=\cos (\pi \sin x)$ then $\sin 2 x$ equals

Question 2:

$\frac{\sec 8 \theta-1}{\sec 4 \theta-1}$ equals

Question 3:

If $\operatorname{cosec} 10^{\circ}-\sqrt{3} \sec 10^{\circ}=k$ then $k$ equals

Question 4:

If $\cos \frac{x}{2} \cdot \cos \frac{x}{2^{2}} \cdot \cos \frac{x}{2^{3}} \cdots \cos \frac{x}{2^{n}} \cdot \sin \frac{x}{2^{n}}$ $=\frac{1}{2^{n}} \cdot f(x)$ where $f(x)$ equals

Question 5:

If $x$ and $y$ be two distinct roots of the equation $p \cos \theta+q \sin \theta=r$ then $\sin (x+y)$ is equal to

Question 6:

Value of $\sin 47^{\circ}+\sin 61^{\circ}-\sin 11^{\circ}-\sin 25^{\circ}$ is

Question 7:

$\sin \frac{\pi}{18} \cdot \sin \frac{5 \pi}{18} \cdot \sin \frac{7 \pi}{18}=\ldots \ldots$

Question 8:

$\sin 157 \frac{1^{\circ}}{2}$ equals

Question 9:

If $\tan \frac{\theta}{2}=\sqrt{\frac{1-e}{1+e}} \times \tan \frac{\phi}{2}$ then $\frac{\cos \theta-e}{1-e \cos \theta}$ equals

Question 10:

If $\tan x \cdot \tan \left(60^{\circ}-x\right) \cdot \tan \left(60^{\circ}+x\right)=\tan n x$ then $\mathrm{n}$ equals.