If operatorname{cosec} theta + cot theta = 5, | vedclass

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(C) Given $\operatorname{cosec} 	heta + \cot 	heta = 5$ $(1)$We know that $\operatorname{cosec}^{2} 	heta - \cot^{2} 	heta = 1$.Using the identity

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$\frac{5}{13}$

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(C) Given $\operatorname{cosec} 	heta + \cot 	heta = 5$ $(1)$We know that $\operatorname{cosec}^{2} 	heta - \cot^{2} 	heta = 1$.Using the identity $a^{2} - b^{2} = (a - b)(a + b)$, we have $(\operatorname{cosec} 	heta - \cot 	heta)(\operatorname{cosec} 	heta + \cot 	heta) = 1$.Substituting $(1)$, we get $(\operatorname{cosec} 	heta - \cot 	heta)(5) = 1 \Rightarrow \operatorname{cosec} 	heta - \cot 	heta = \frac{1}{5}$ $(2)$.Adding $(1)$ and $(2)$, we get $2 \operatorname{cosec} 	heta = 5 + \frac{1}{5} = \frac{26}{5}$.Therefore, $\operatorname{cosec} 	heta = \frac{13}{5}$.Since $\sin 	heta = \frac{1}{\operatorname{cosec} 	heta}$, we have $\sin 	heta = \frac{5}{13}$.

If $\operatorname{cosec} \theta + \cot \theta = 5$, then $\sin \theta = $

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