cosec theta upon cosec theta - 1 + cosec theta upon cosec theta +1 = 2 sec square theta
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Answer:
Here I used A instead of theta.
LHS= CosecA/(cosecA-1)+cosecA/(cosecA+1 )
= CosecA [1/(cosecA-1) +1/(Cosec A+1)]
= CosecA[(cosecA+1+cosec A -1)/(cosecA-1 )(cosec A+1 )]
= ( 2cosec²A ) / [ cosec² A - 1 ]
= 2cosec²A / cot² A
= 2 ( 1/sin² A ) / ( cos² A/sin² A )
= 2/cos² A
= 2sec²A
= RHS
Hope it helps you
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