Question

How do I prove this equation is an identity? Sin(x)/csc(x)+Cos(x)/Sec(x)=1

Answer 1

Below.

Explanation:

`csc(x)=1/sin(x)`
`sec(x)=1/cos(x)`
`therefore sin(x)/csc(x)=sin(x)/(1/sin(x))=sin^2(x)`

Similarly,

`cos(x)/sec(x)=cos(x)/(1/sec(x))=cos^2(x)`

Therefore,

`LHS=sin(x)/csc(x)+cos(x)/sec(x)=sin^2(x)+cos^2(x)=1=RHS`