If {left( {frac{{sin theta }}{{sin phi }}} ri | vedclass

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Question

(a) ${\left( {\frac{{\sin 	heta }}{{\sin \phi }}} ight)^2} = \frac{{	an 	heta }}{{	an \phi }}$
$ \Rightarrow $ $\sin 	heta .\cos 	heta = \sin

Vedclass · Accepted Answer

$	heta = n\pi \pm \frac{\pi }{3},\,\phi = n\pi \pm \frac{\pi }{6}$

Vedclass · Answer

(a) ${\left( {\frac{{\sin 	heta }}{{\sin \phi }}} ight)^2} = \frac{{	an 	heta }}{{	an \phi }}$
$ \Rightarrow $ $\sin 	heta .\cos 	heta = \sin \phi \cos \phi $
$ \Rightarrow $ $\sin 2	heta = \sin 2\phi $
$2	heta = \pi - 2\phi $ $ \Rightarrow $ $	heta = \frac{\pi }{2} - \phi $
But $\frac{{	an 	heta }}{{	an \phi }} = 3$ $ \Rightarrow $ $\frac{{	an 	heta }}{{\cot 	heta }} = 3$ $ \Rightarrow $ ${	an ^2}	heta = 3$
$ \Rightarrow $ $	heta = n\pi \pm \frac{\pi }{3}$, so that $\phi = n\pi \pm \frac{\pi }{6}$.
Trick : Check with the options for $n = 0,\,1$.

If ${\left( {\frac{{\sin \theta }}{{\sin \phi }}} \right)^2} = \frac{{\tan \theta }}{{\tan \phi }} = 3,$ then the value of $\theta $ and $\phi $ are

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