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

Question

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

Aicharya · Accepted Answer

Given $\operatorname{cosec} 	heta+\cot 	heta=5$ We know that $\operatorname{cosec}^{2} 	heta-\cot ^{2} 	heta=1$ $\Rightarrow(\operatorname{cosec} 	heta-\cot 	heta)(\operatorname{cosec} 	heta+\cot 	heta)=1 \Rightarrow \operatorname{cosec} 	heta-\cot 	heta=\frac{1}{5}$ Adding (1) \& (2), we get $2 \operatorname{cosec} 	heta=5+\frac{1}{5}=\frac{26}{5}$ $	herefore \operatorname{cosec} 	heta=\frac{13}{5} \Rightarrow \sin 	heta=\frac{5}{13}$

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

Solution