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\frac { \operatorname { cosec } \theta } { \operatorname { cosec } - 1 } + \frac { \operatorname { cosec } \theta } { \operatorname { cosec } \theta + 1 } = 2 \operatorname { sec } ^ { 2 } \theta |
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Answer» 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 |
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