Prove the following identities.(1+sinx)(1−cos2x)(1+cosx)(1+cos2x)=1−cosx1−sinx

LHS=(1+sinx)(1−cos2x)(1+cosx)(1+cos2x)=(1+sinx)2.sin2x(1+cosx)2.cos2x=(1+sinx)(1−cos2x)(1+cosx)(1−sin2x)=(1+sinx)(1−cosx)(1+cosx)(1+cosx)(1−sinx)(1+sinx)=1−cosx1−sinx=RHS

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Prove the following identities. , {(1 , + , cos , x)(1 , + , c

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Prove the following identities.
$\frac{( 1 + cos x ) ( 1 + cos 2 x )}{( 1 + s in x ) ( 1 - cos 2 x )} = \frac{1 - s in x}{1 - cos x}$

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Prove the following identities.

\frac{( 1 + cos x ) ( 1 + cos 2 x )}{( 1 + s in x ) ( 1 - cos 2 x )} = \frac{1 - s in x}{1 - cos x}

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Text solutionVerified

L H S = \frac{( 1 + cos x ) ( 1 + cos 2 x )}{( 1 + sin x ) ( 1 - cos 2 x )}

= \frac{( 1 + cos x ) 2. cos ^{2} x}{( 1 + sin x ) 2. sin ^{2} x}

= \frac{( 1 + cos x ) ( 1 - sin ^{2} x )}{( 1 + sin x ) ( 1 - cos ^{2} x )}

= \frac{( 1 + cos x ) ( 1 - sin x ) ( 1 + sin x )}{( 1 + sin x ) ( 1 - cos x ) ( 1 + cos x )}

= \frac{1 - sin x}{1 - cos x} = R H S

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Question Text	Prove the following identities. $\frac{( 1 + cos x ) ( 1 + cos 2 x )}{( 1 + s in x ) ( 1 - cos 2 x )} = \frac{1 - s in x}{1 - cos x}$
Answer Type	Text solution:1
Upvotes	150

Prove the following identities.(1+sinx)(1−cos2x)(1+cosx)(1+cos2x)​=1−cosx1−sinx​

Text solutionVerified

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Prove the following identities.
$\frac{( 1 + cos x ) ( 1 + cos 2 x )}{( 1 + s in x ) ( 1 - cos 2 x )} = \frac{1 - s in x}{1 - cos x}$