Question

Show that under root 1- sin Tetha/1+ sin tetha = Sec tetha - tan Tetha

Answer 1

Hello friend

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here is your answer!!!!

===>
$\sqrt{ \frac{1 - sin \: tetha}{1 + \sin \: tetha \: } } \times \frac{1 - sin \: tetha \: }{1 - sin \: tetha} \\ \\ = \sqrt{ \frac{(1 - sin \: tetha \:) {}^{2} }{1 - sin {}^{2} \: tetha} } \\ \\ = \sqrt{ \frac{(1 - sin \: tetha) {}^{2} }{cos {}^{2} \: tetha} } \\ \\ = \frac{1 - sin \: tetha}{cos \: tetha} \\ \\ = \frac{1}{cos \: tetha} - \frac{sin \: tetha}{cos \: tetha} \\ \\ = sec \: tetha \: - tan \: tetha$
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