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 identit

Vedclass · Accepted Answer

$\frac{5}{13}$

Vedclass · Answer

(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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