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Question

(cosecA-cotA)2=1-cosA/1+cosA

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Solution

L.H.S.= (cosecA-cotA)2

=( 1/ sinA - cosA/sinA )²

= ( 1 - cosA/ sinA )²

= ( 1 + cosA )²/ sin²A

= ( 1 - cosA )²/ 1 - cos²A

= ( 1 - cosA ) ( 1 - cosA )/ ( 1 + cosA ) ( 1 - cosA )

= 1 - cosA / 1 + cosA

= R.H.S

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