The value of 1-cos- 1-cos- isa -cosec-b cosec-c cosec2- 2-d -cosec-2

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Calculating Heights and Distances

The value of ...

Question

The value of $\sqrt{\frac{1 + \cos θ}{1 - \cos θ}}$ is

(a) cot θ − cosec θ
(b) cosec θ + cot θ
(c) cosec² θ + cot² θ
(d) (cot θ + cosec θ)²

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Solution

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(i) \sqrt{\frac{1 + \sin θ}{1 - \sin θ}} = (\sec θ + \tan θ) (ii) \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = (cosec θ - \cot θ) (iii) \sqrt{\frac{1 + \cos θ}{1 - \cos θ}} + \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = 2 cosec θ

\sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = cosec θ - \cot θ

\frac{1 - sinθ}{1 + sinθ} = (secθ - tanθ)^{2}

\frac{1 + cosθ}{1 - cosθ} = (cosecθ + cotθ)^{2}

(cot θ - c o s e c θ)^{2} = \frac{1 - cos θ}{1 + cos θ}

cos θ = \frac{3}{4}

\sqrt{\frac{sec θ - c o s e c θ}{sec θ + c o s e c θ}}

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