How do you verify the identity: (secx + cscx )/( sinx + cosx) = cotx + tanx? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Abhishek K. Jul 15, 2018 LHS=(secx+cscx)/(sinx+cosx) =(1/cosx+1/sinx)/(sinx+cosx) =(cancel((sinx+cosx))/(sinxcosx))/(cancel((sinx+cosx))/1) =1/(sinxcosx) =(sin^2x+cos^2x)/(sinxcosx)=sin^2x/(sinxcosx)+cos^2x/(sinxcosx)=cotx+tanx=RHS Answer link Related questions What does it mean to prove a trigonometric identity? How do you prove \csc \theta \times \tan \theta = \sec \theta? How do you prove (1-\cos^2 x)(1+\cot^2 x) = 1? How do you show that 2 \sin x \cos x = \sin 2x? is true for (5pi)/6? How do you prove that sec xcot x = csc x? How do you prove that cos 2x(1 + tan 2x) = 1? How do you prove that (2sinx)/[secx(cos4x-sin4x)]=tan2x? How do you verify the identity: -cotx =(sin3x+sinx)/(cos3x-cosx)? How do you prove that (tanx+cosx)/(1+sinx)=secx? How do you prove the identity (sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)? See all questions in Proving Identities Impact of this question 11301 views around the world You can reuse this answer Creative Commons License