Question

$\frac{1-rcos\alpha }{rsin\alpha }$ is equal tto

• A. $tan2\theta$
• B. $cot2\theta$
• C. $sin2\theta$
• D. $cos2\theta$

Answer 1

Answer: (A)

$tan2\theta$

In $△OLC$
$OL=rcos(\alpha -3\theta ),CL=rsin(\alpha -3\theta )$
Therefore,
$\frac{si{n}^3\theta }{rsin(\alpha -3\theta )}=\frac{co{s}^3\theta }{rcos(\alpha -3\theta )}=1\Rightarrow \frac{si{n}^3\theta }{sin(\alpha -3\theta )}=\frac{co{s}^3\theta }{cos(\alpha -3\theta )}=r\Rightarrow co{s}^4\theta -si{n}^4\theta =cos\theta \left(rcos(\alpha -3\theta )\right)-sin\theta \left(rsin(\alpha -3\theta )\right)\Rightarrow cos2\theta =rcos(\alpha -2\theta )\Rightarrow cos2\theta =r(cos\alpha cos2\theta +sin\alpha sin2\theta )\Rightarrow (1-rcos\alpha )cos2\theta =rsin\alpha sin2\theta \Rightarrow \frac{1-rcos\alpha }{rsin\alpha }=tan2\theta$