Question

1/(sin a+ cos a)+(1/sina -cos a)=2 sin a/1-2cos square a​

Answer 1

Hi !

From LHS :-

= 1/(sinA+ cosA) + 1/(sinA- cosA)

= SinA-cosA+sinA+cosA/(sin²A - cos²A) , {LCM taken }

= 2sinA/(1-cos²A-cos²A) °•° sin²A= 1-cos²A

= 2sinA/ 1-2cos²A

LHS = RHS PROVED

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Hope it's helpful

Answer 2

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$\bold{\huge{\underline{\underline{\rm{ LHS :}}}}}$

$= \frac{1}{sin \: a + cos \: a} + \frac{1}{sin \: a - cos \: a} \\ = \frac{sin \: a - cos \: a + sin \: a + cos \: a}{(sin \: a + cos \: a)(sin \: a - cos \: a)} \\ = \frac{2sin \: a}{ {sin }^{2} a - {cos}^{2}a } \\ = \frac{2 \: sin \: a}{1 - {cos}^{2}a - {cos}^{2}a } \\ = \frac{2 \: sin \: a}{1 - 2 {cos}^{2} a}$

$\bold{\huge{\underline{\underline{\rm{ RHS :}}}}}$

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