Question

Prove that (cosec A − sin A) (sec A − cos A) = 1 / (tanA + cotA)

Answer 1

Hi ,

LHS = ( cosecA - sinA )( SecA - cosA )

= ( cosecA - 1/cosecA ) ( secA - 1/secA )

= [( cosec²A - 1 )/cosecA ][ ( sec²A - 1 )/secA ]

= ( cot²A /cosecA )( tan² A /secA )

= ( cot²A tan²A )/( cosecAsecA )

= 1/cosecAsecA

= sinAcosA ----( 1 )

RHS = 1/( tanA + cotA )

= 1/[ sinA/cosA + cosA/sinA ]

= 1/[ ( sin²A + cos²A )/( cosAsinA ) ]

= 1/[ 1/sinAcosA ]

= sinAcosA --( 2 )

( 1 ) = ( 2 )

LHS = RHS

I hope this helps you.

: )

Answer 2

answer is

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(1):(2)

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