MCQ
${{(\sin \theta +i\,\cos \theta )}^{n}}\,$is equal to [RPET 2001]
- A$\cos n\theta +i\,\sin n\theta $
- B$\sin n\theta +i\,\cos n\theta $
- ✓$\cos n\left( \frac{\pi }{2}-\theta \right)+i\,\sin n\left( \frac{\pi }{2}-\theta \right)$
- DNone of these
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If A and B are coefficient of xn in the expansions of (1 + x)2n and (1 + x)2n – 1 respectively, then $\frac{\text{A}}{\text{B}}$ equals:
$1.$
$2.$
$\frac{1}{2}.$
$\frac{1}{\text{n}}.$
Hint:
$\frac{\text{A}}{\text{B}}=\frac{^{2\text{n}}\text{C}_\text{n}}{^{2\text{n}-1}\text{C}_\text{n}}=2$If a line makes an angle a with the positive direction of x-axis, then the slope of the line is given by: