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. · 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 6222 views around the world You can reuse this answer Creative Commons License