If $ an heta+\sin heta=a$ and $ an heta-\sin heta=b$, then the values of $\cot heta$ and $\operatorname{cosec} heta$ are respectively

Question

If $	an 	heta+\sin 	heta=a$ and $	an 	heta-\sin 	heta=b$, then the values of $\cot 	heta$ and $\operatorname{cosec} 	heta$ are respectively

Aicharya · Accepted Answer

We have $	an 	heta+\sin 	heta=a\ldots(1)$ and $	an 	heta-\sin 	heta=b\ldots(2)$ Adding equation (1) \& (2), we get $2 	an 	heta=a+b \Rightarrow 	an 	heta=\frac{a+b}{2} \Rightarrow \cot 	heta=\frac{2}{a+b}$ By equation (1) - equation (2), we get $2 \sin 	heta=a-b \quad \Rightarrow \sin 	heta=\frac{a-b}{2} \Rightarrow \operatorname{cosec} 	heta=\frac{2}{a-b}$

If $\tan \theta+\sin \theta=a$ and $\tan \theta-\sin \theta=b$, then the values of $\cot \theta$ and…

Solution