If $\sec heta=\frac{13}{12}, heta$ lies in $4^{ ext {th }}$ quadrant, then $ an heta imes \operatorname{cosec} heta imes \sin heta imes \cos heta=$

Question

If $\sec 	heta=\frac{13}{12}, 	heta$ lies in $4^{	ext {th }}$ quadrant, then $	an 	heta 	imes \operatorname{cosec} 	heta 	imes \sin 	heta 	imes \cos 	heta=$

Aicharya · Accepted Answer

Given $\sec 	heta=\frac{13}{12} \Rightarrow \cos 	heta=\frac{12}{13}$ $	herefore \sin 	heta=\sqrt{1-\frac{144}{169}}=-\frac{5}{13} \quad \ldots\left[	hetaight.$ lies in $4^{	ext {th }}$ quadrant $]$ $	an 	heta=\frac{\left(\frac{5}{13}ight)}{\left(\frac{12}{13}ight)}=\frac{-5}{12}$ and $\operatorname{cosec} 	heta=\frac{-13}{5}$ $	herefore \quad 	an 	heta 	imes \operatorname{cosec} 	heta 	imes \sin 	heta 	imes \cos 	heta=\left(\frac{-5}{12}ight) 	imes\left(\frac{-13}{5}ight) 	imes\left(\frac{-5}{13}ight)\left(\frac{12}{13}ight)=\frac{-5}{13}$

If $\sec \theta=\frac{13}{12}, \theta$ lies in $4^{\text {th }}$ quadrant, then $\tan \theta \times…

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