How do I prove this equation is an identity? Sin(x)/csc(x)+Cos(x)/Sec(x)=1 Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Nolan Y. ยท Stefan V. Mar 22, 2018 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 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 6705 views around the world You can reuse this answer Creative Commons License