Sin theta + cosec theta/sin theta=2+cot^theta
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let theta =@
LHS =(sin@+cosec@)/sin@
=sin@/sin@+cosec@/sin@
=1 +1/sin^2@
=1 + cosec^2@
=1+(1+cot^2@)
because
cosec^2x-cot^2x=1
so, cosec^2x=1+cot^2@
now ,
=2+cot^2@=RHS
LHS =(sin@+cosec@)/sin@
=sin@/sin@+cosec@/sin@
=1 +1/sin^2@
=1 + cosec^2@
=1+(1+cot^2@)
because
cosec^2x-cot^2x=1
so, cosec^2x=1+cot^2@
now ,
=2+cot^2@=RHS
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