જો theta એ બીજા ચરણમાં હોય તો sq | vedclass

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Question

(b) $\sqrt {\left( {\frac{{1 - \sin 	heta }}{{1 + \sin 	heta }}} ight)} + \sqrt {\left( {\frac{{1 + \sin 	heta }}{{1 - \sin 	heta }}} ight)} $

Vedclass · Accepted Answer

$ - 2\sec 	heta $

Vedclass · Answer

(b) $\sqrt {\left( {\frac{{1 - \sin 	heta }}{{1 + \sin 	heta }}} ight)} + \sqrt {\left( {\frac{{1 + \sin 	heta }}{{1 - \sin 	heta }}} ight)} $

is the sum of two positive quantities and hence the result must be positive.

But for $\frac{\pi }{2} < 	heta < \pi ,$

we have the sum equal to $\frac{{1 - \sin 	heta + 1 + \sin 	heta }}{{\sqrt {1 - {{\sin }^2}	heta } }} = \frac{2}{{\cos 	heta }};$

which is negative.

($\because$  $\cos 	heta $ is negative for $	heta$ lying in $2^{nd}$ quadrant).

So the required positive value $ = \frac{{ - 2}}{{\cos 	heta }} = - 2\,\sec 	heta ,\,\left( {\frac{\pi }{2} < 	heta < \pi } ight)$.

જો $\theta $ એ બીજા ચરણમાં હોય તો $\sqrt {\left( {\frac{{1 - \sin \theta }}{{1 + \sin \theta }}} \right)} + \sqrt {\left( {\frac{{1 + \sin \theta }}{{1 - \sin \theta }}} \right)} $ ની કિમત મેળવો.

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