Question

Prove that sin A(1/sinA-1/cosec A)= cos 2 A

Answer 1

Answer:1+cosec A)/ cosecA = cos2A/( sinA-1)

LHS:

(1+cosecA)/cosec A

= (1/cosecA) + (cosecA/cosecA)

= sinA+1

=sinA+1 X (1-sinA/1-sinA)

=sin2A-1/1-sinA

=cos2A/1-sinA

=RHS.

Hence Proved

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