If cosec - cot = p, then the value of cosec is

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Solution

Q.
If $cosec θ - \cot θ = p,$ then the value of $cosec θ$ is

1 $\frac{1}{2} (p + \frac{1}{p})$

2 $\frac{1}{2} (1 - \frac{1}{p})$

3 $(1 + \frac{1}{p})$

4 $(1 - \frac{1}{p})$

Ans.
(1)

Since $cosec θ - \cot θ = p$

$\Rightarrow$ $cosec θ + \cot θ = \frac{1}{p}$

Adding (i) and (ii), we have

$2 cosec θ = p + \frac{1}{p}$

$∴$ $cosec θ = \frac{1}{2} (p + \frac{1}{p})$

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