Question #7cb8c

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Answer 1 · 2017-01-31T02:40:11

see explanation

$\sqrt{\frac{1 + cos θ}{1 - cos θ}}$ $sqrt((1+cos theta)/(1-cos theta))$

multiply with $\sqrt{1 + cos θ}$ $sqrt (1+cos theta)$

$\sqrt{\frac{1 + cos θ}{1 - cos θ}} \cdot \sqrt{\frac{1 + cos θ}{1 + cos θ}}$ $sqrt((1+cos theta)/(1-cos theta))*sqrt((1+cos theta)/(1+cos theta))$

$\sqrt{(\frac{1 + cos θ}{1 - cos θ}) \cdot (\frac{1 + cos θ}{1 + cos θ})}$ $sqrt(((1+cos theta)/(1-cos theta))*((1+cos theta)/(1+cos theta))$

$= \sqrt{\frac{{(1 + cos θ)}^{2}}{(1 - {cos}^{2} θ)}}$ $= sqrt((1+cos theta)^2/((1-cos^2 theta))$

$= \sqrt{\frac{{(1 + cos θ)}^{2}}{{sin}^{2} θ}} = \frac{1 + cos θ}{sin θ}$ $= sqrt((1+cos theta)^2/sin^2 theta) = (1+cos theta)/sin theta$

$= \frac{1}{sin θ} + \frac{cos θ}{sin θ}$ $= 1/sin theta +cos theta/sin theta$

$= cos e c θ + cot θ$ $=cosec theta + cot theta$