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

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(C) Given that $\operatorname{cosec} 	heta + \cot 	heta = p$. We know the identity $\operatorname{cosec}^{2} 	heta - \cot^{2} 	heta = 1$,which can

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$\frac{p^{2} - 1}{p^{2} + 1}$

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(C) Given that $\operatorname{cosec} 	heta + \cot 	heta = p$. We know the identity $\operatorname{cosec}^{2} 	heta - \cot^{2} 	heta = 1$,which can be written as $(\operatorname{cosec} 	heta - \cot 	heta)(\operatorname{cosec} 	heta + \cot 	heta) = 1$. Substituting the given value,we get $\operatorname{cosec} 	heta - \cot 	heta = \frac{1}{p}$. Now,adding the two equations: $(\operatorname{cosec} 	heta + \cot 	heta) + (\operatorname{cosec} 	heta - \cot 	heta) = p + \frac{1}{p} \Rightarrow 2 \operatorname{cosec} 	heta = \frac{p^{2} + 1}{p} \Rightarrow \operatorname{cosec} 	heta = \frac{p^{2} + 1}{2p}$. Subtracting the two equations: $(\operatorname{cosec} 	heta + \cot 	heta) - (\operatorname{cosec} 	heta - \cot 	heta) = p - \frac{1}{p} \Rightarrow 2 \cot 	heta = \frac{p^{2} - 1}{p} \Rightarrow \cot 	heta = \frac{p^{2} - 1}{2p}$. Finally,$\cos 	heta = \frac{\cot 	heta}{\operatorname{cosec} 	heta} = \frac{(p^{2} - 1) / 2p}{(p^{2} + 1) / 2p} = \frac{p^{2} - 1}{p^{2} + 1}$.

If $\operatorname{cosec} \theta + \cot \theta = p,$ then $\cos \theta =$

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