Question

Prove the identity cot^2x/cscx+1=1-sinx/sinx

Answer 1

Cot²x/csc+1
=(csc²x-1)/(csc+1)

=((1/sin²x)-1)/((1/sinx)+1)

=((1-sin²x)/sin²x)/((1+sinx)/sinx)

=(1-sin²x)/(1+sinx)

=(1+sinx)(1-sinx)/sinx(1+sinx)

=(1-sinx)/sinx