If operatorname{cosec} theta - cot theta = p, | vedclass

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(A) Given that $\operatorname{cosec} 	heta - \cot 	heta = p$  (Equation $1$).We know the trigonometric identity $\operatorname{cosec}^2 	heta - \co

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Given that $\operatorname{cosec} 	heta - \cot 	heta = p$  (Equation $1$).We know the trigonometric identity $\operatorname{cosec}^2 	heta - \cot^2 	heta = 1$.This can be written as $(\operatorname{cosec} 	heta - \cot 	heta)(\operatorname{cosec} 	heta + \cot 	heta) = 1$.Substituting the value of $p$ from Equation $1$,we get $p(\operatorname{cosec} 	heta + \cot 	heta) = 1$.Therefore,$\operatorname{cosec} 	heta + \cot 	heta = \frac{1}{p}$ (Equation $2$).Adding Equation $1$ and Equation $2$:$(\operatorname{cosec} 	heta - \cot 	heta) + (\operatorname{cosec} 	heta + \cot 	heta) = p + \frac{1}{p}$.$2 \operatorname{cosec} 	heta = p + \frac{1}{p}$.$\operatorname{cosec} 	heta = \frac{1}{2} \left( p + \frac{1}{p} ight)$.

If $\operatorname{cosec} \theta - \cot \theta = p$,then the value of $\operatorname{cosec} \theta =$

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