Prove that tan^2(x)=1/(cos^2(x))-1

tan^2(x)=1/(cos^2(x))-1 Left hand side of the equation (LHS)=tan^2(x) Use the identity tan(x)=sin(x)/cos(x) and substitute it into the LHS LHS=sin^2(x)/cos^2(x) Use the identity sin^2(x)+cos^2(x)=1 and rearrange to make sin^2(x) the subject sin^2(x)=1-cos^2(x) Substitute this into the LHS: sin^2(x)/cos^2(x)=1-cos^2(x)/cos^2(x) Simplify this to give the RHS of the equation given:1-cos^2(x)/cos^2(x)=1/(cos^2(x))-1 Therefore the LHS=RHS