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3.Trigonometrical Ratios, Functions and Identities
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यदि $\frac{{2\sin \alpha }}{{\{ 1 + \cos \alpha + \sin \alpha \} }} = y,$ हो, तो $\frac{{\{ 1 - \cos \alpha + \sin \alpha \} }}{{1 + \sin \alpha }} $ बराबर है
A
$\frac{1}{y}$
B
$y$
C
$1 - y$
D
$1 + y$
Solution
(b) यहाँ, $\frac{{2\sin \alpha }}{{1 + \cos \alpha + \sin \alpha }} = y$
तब $\frac{{4\sin \frac{\alpha }{2}\cos \frac{\alpha }{2}}}{{2{{\cos }^2}\frac{\alpha }{2} + 2\sin \frac{\alpha }{2}\cos \frac{\alpha }{2}}} = y$
==> $\frac{{2\sin \frac{\alpha }{2}}}{{\cos \frac{\alpha }{2} + \sin \frac{\alpha }{2}}} \times \frac{{\left( {\sin \frac{\alpha }{2} + \cos \frac{\alpha }{2}} \right)}}{{\left( {\sin \frac{\alpha }{2} + \cos \frac{\alpha }{2}} \right)}} = y$
==> $\frac{{1 – \cos \alpha + \sin \alpha }}{{1 + \sin \alpha }} = y$.
Standard 11
Mathematics