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If we take L.H.S.,
L.H.S = ( 1 + 1/tan^2A ) ( 1 + 1/cot^2A)
= ( tan^2A + 1 )/tan^2A × ( cot^2A + 1 )/cot^2A
= sec^2A/tan^2A × cosec^2A/cot^2A
= sec^2A × cosec^2A.........because tanA × cotA = 1
= 1 / ( cos^2A × sin^2A )
= 1 / { (1-sin^2A)×sin^2A }
L.H.S. = 1 / ( sin^2A - sin^4A) = R.H.S.
Hence Proved.........●
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Hope it was helpful.
L.H.S = ( 1 + 1/tan^2A ) ( 1 + 1/cot^2A)
= ( tan^2A + 1 )/tan^2A × ( cot^2A + 1 )/cot^2A
= sec^2A/tan^2A × cosec^2A/cot^2A
= sec^2A × cosec^2A.........because tanA × cotA = 1
= 1 / ( cos^2A × sin^2A )
= 1 / { (1-sin^2A)×sin^2A }
L.H.S. = 1 / ( sin^2A - sin^4A) = R.H.S.
Hence Proved.........●
●●●●●●●●●●●●●●●●●
Hope it was helpful.
SidVK:
Hello Sneha! Is There sign of minus with 1 or not?
no thanks a lot
Ohh...You are always welcome ! ^_^
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