Question

sin A/(cot A + cosec A) =2+(sin A /cot A - cosec A)​

Answer 1

LHS

=sinA/cotA+cosecA

=sinA/(cosA/sinA+1/sinA)

=sinA/{(cosA+1)/sinA}

=sin²A/(1+cosA)

=(1-cos²A)/(1+cosA)

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

=1-cosA

RHS

=2+sinA/cotA-cosecA

=2+sinA/(cosA/sinA-1/sinA)

=2+sinA/{(cosA-1)/sinA}

=2+sin²A/{-(1-cosA)}

=2-{(1-cos²A)/(1-cosA)}

=2-{(1+cosA)(1-cosA)/(1-cosA)}

=2-(1+cosA)

=2-1-cosA

=1-cosA

∴, LHS=RHS

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Answer 2

Answer:

Step-by-step explanation: