prove that 1+sin(x)/cos(x)=sin(x)/1-sin(x)

Question

Prove that they equal each other by solving the left side.

Answer 1

When x=0, the left-hand side = 1 but the right-hand side is zero, so this is not an identity, but an equation.

Multiply through by 1-sinx: (1-sin^2x)/cosx=sinx; cos^2x/cosx=cosx (left-hand side)=sinx (right-hand side).

Divide through by cosx: tanx=1 so x=45 degrees.