Question

prove that (cosec a/cosec a+1)+(coseca/coseca-1)=2sec`2a

Answer 1

GIVEN :- {cosec A/cosec A+1}+{cosec A/cosec A-1}

TO PROVE :- 2 sec^2 a

PROOF :-

cosec A = 1/sin A ||| equation 1

{1/sin A/1+sin A/sin A}+{1/sin A/1-sin A/sin A} ||| from eq.1

{1/1+sin A} + {1/1-sin A} ||| cancelling sin A

{1+sin A+1-sin A}/{1-sin^2 A} ||| taking L.C.M.

2/cos^2 A ||| 1-sin^2 A=cos^2 A

2 sec ^2 A ||| 1/cos^2 A = sec ^2 A

HENCE PROVED

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Answer 2

Answer:

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