Prove that sinA1+cosA+1+cosAsinA=2cscA

LHS = sinA1+cosA+1+cosAsinA=sinA(1+cosA)(1+cosA)2+sin2A=sinA(1+cosA)1+2cosA+cos2A+sin2A=sinA(1+cosA)1+2cosA+1[sin2A+cos2A=1]=sinA(1+cosA)2+2cosA=sinA(1+cosA)2[1+cosA]=sinA2=2cosecA=RHSLHS = RHS Hence proved.

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

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

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Prove that

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

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Text solutionVerified

LHS =

\frac{1 + cos A}{s in A} + \frac{s in A}{1 + cos A}

= \frac{( 1 + cos A ) ^{2} + s i n ^{2} A}{s in A ( 1 + cos A )}

= \frac{1 + 2 cos A + co s ^{2} A + s i n ^{2} A}{s in A ( 1 + cos A )}

= \frac{1 + 2 cos A + 1}{s in A ( 1 + cos A )} [s i n^{2} A + co s^{2} A = 1]

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

= \frac{2 [ 1 + cos A ]}{s in A ( 1 + cos A )}

= \frac{2}{s in A}

= 2 cosec A = R H S

LHS = RHS

Hence proved.

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

Prove that sinA1+cosA​+1+cosAsinA​=2cscA

Text solutionVerified

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