Question

Any genius here to prove this.....!

Answer 1

Hey friends ☺ by the I am not a genius but I can try to solve it

From LHS

1/cosecx+cotx-1/sinx

=1/cosecx+cotx×cosecx-cotx/cosecx-cotx-1/sinx, (multiplying by cosecx -cotx on 1/cosecx +cotx}

we get,

cosecx-cotx/cosec²x-cot-1/sinx

=>cosecx-cotx-cosecx

=>-cotx

Now from RHS

1/sinx-1/cosecx-cotx

=>cosecx-1/cosecx-cotx×cosecx+cotx

{multiplying by cosecx+ cotx on cosecx-cosecx -cotx}

==>cosecx-(cosecx+cotx)/cosec²x-cot²x)

{•°•cosec²x-cot²x=1}

=>cosecx-cosecx-cotx /1

=>-cotx

here prooved

LHS=RHS,

Hope it helps you .

@Rahukumar 111