How do I prove this is an identity? 1/csc(theta)/csc(theta)-cot(theta)=1+cos(theta)/sin(theta)

2 Answers
Mar 23, 2018

This is not an identity...

Explanation:

LHS "" =>1/(csctheta/csctheta)-cottheta

=>1/(cancelcsctheta/cancelcsctheta)-cottheta

=>1/1-cottheta

RHS=>1+costheta/sintheta

=>1+cottheta

LHS !=RHS

Mar 23, 2018

See the explanation

Explanation:

LHS = 1/(csctheta-cottheta

Substitute 1 with (csc^2theta-cot^2theta)

=> (csc^2theta-cot^2theta)/(csctheta-cottheta

=> ((csctheta-cottheta)(csctheta+cottheta))/(csctheta-cottheta

=> [(cancel(csctheta-cottheta))(csctheta+cottheta)]/cancel((csctheta-cottheta)

=> csctheta+cottheta

RHS = (1+costheta)/sintheta

=> 1/sintheta + costheta/sintheta

=> csctheta+cottheta

Hence , LHS=RHS