Question 622088
cosx(tan^2x+1)=secx


cosx*tan^2x+cosx=secx


cosx*(sin^2x)/(cos^2x)+cosx=secx


(sin^2x)/(cosx)+cosx=secx


(sin^2x)/(cosx)+cosx*(cosx)/(cosx)=secx


(sin^2x)/(cosx)+(cos^2x)/(cosx)=secx


(sin^2x+cos^2x)/(cosx)=secx


1/(cosx)=secx


secx=secx


So this verifies the identity.