Question

1/cosecA - cot A - 1/sin A
=1/sin A - 1/cosecA + cot A
​

Answer 1

Solution:

LHS = 1/cosec A - cot A - 1/sin A

= 1/cosec A - cot A × cosec A + cot A/cosec A + cot A - 1/sin A

= ( cosec A + cot A )/( cosec^2A - cot^2A ) - 1/sin A

= ( cosec A + cot A )/( cosec^2A - cot^2A ) - cosec A

= cosec A + cot A - cosec A

= cot A

RHS = 1/sin A - 1/cosecA + cot A

= cosec A - ( cosec A + cot A )/( cosec^2A - cot^2A )

= cosec A - ( cosec A - cot A )

= cosec A - cosec A + cot A

= cot A

So, LHS = RHS

Hence proved

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