Prove sinA1+cosA+1+cosAsinA=2cosecA

L.H.S. =sinA1+cosA+1+cosAsinA=sinA(1+cosA)(1+cosA)(1+cosA)+sinAsinA=(1+cosA)sinA(1+cosA)2+sin2A=(1+cosA)sinA1+cos2A+2cosA+sin2A=(1+cosA)sinA1+2cosA+1=(1+cosA)sinA2+2cosA=(1+cosA)sinA2(1+cosA)=2sinA1=2cosecA=R.H.SHence proved.

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Prove {{1 + A}}{{ A}} + {{ A}}{{1 + A}} = 2{cosec}A

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Prove $\frac{1 + cos A}{sin A} + \frac{sin A}{1 + cos A} = 2 cosec A$

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\frac{1 + cos A}{sin A} + \frac{sin A}{1 + cos A} = 2 cosec A

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Text solutionVerified

L.H.S.

= \frac{1 + cos A}{sin A} + \frac{sin A}{1 + cos A}

= \frac{( 1 + cos A ) ( 1 + cos A ) + sin A sin A}{sin A ( 1 + cos A )}

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

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

= \frac{1 + 2 cos A + 1}{( 1 + cos A ) sin A}

= \frac{2 + 2 cos A}{( 1 + cos A ) sin A}

= \frac{2 ( 1 + cos A )}{( 1 + cos A ) sin A}

= 2 \frac{1}{sin A}

= 2 cosec A

=

R.H.S

Hence proved.

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Question Text	Prove $\frac{1 + cos A}{sin A} + \frac{sin A}{1 + cos A} = 2 cosec A$
Answer Type	Text solution:1
Upvotes	150

Prove sinA1+cosA​+1+cosAsinA​=2cosecA

Text solutionVerified

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Prove $\frac{1 + cos A}{sin A} + \frac{sin A}{1 + cos A} = 2 cosec A$