If $ heta$ is an acute angle, $\cos h x=K$ and $\sin h x= an heta$, then $\sin heta=$

Question

If $	heta$ is an acute angle, $\cos h x=K$ and $\sin h x=	an 	heta$, then $\sin 	heta=$

Aicharya · Accepted Answer

$\cosh x=K$
Since, $\cos h ^2 x+\sin h^2 x=1$ $\Rightarrow \sinh x=\sqrt{K^2-1} \Rightarrow \tan \theta=\frac{\sqrt{K^2-1}}{1}=\frac{P}{B}$ Let $\mathrm{P}=\lambda \sqrt{K^2-1}, \mathrm{~B}=\lambda \Rightarrow \mathrm{H}=\lambda K$ $\Rightarrow \sin \theta=\frac{\mathrm{P}}{\mathrm{H}}=\frac{\sqrt{K^2-1}}{K}$

If $\theta$ is an acute angle, $\cos h x=K$ and $\sin h x=\tan \theta$, then $\sin \theta=$

Solution