Prove that #(cotx-tanx)/(sinx+cosx)=cscx-secx#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Shwetank Mauria May 3, 2016 Please see below. Explanation: #(cotx-tanx)/(sinx+cosx)# = #(cosx/sinx-sinx/cosx)/(sinx+cosx)# = #((cos^2x-sin^2x)/(sinxcosx))/(sinx+cosx)# = #((cosx-sinx)(cosx+sinx))/(sinxcosx)xx1/(sinx+cosx)# = #((cosx-sinx)cancel((cosx+sinx)))/(sinxcosx)xx1/cancel((sinx+cosx))# = #((cosx-sinx))/(sinxcosx)# = #cosx/(sinxcosx)-sinx/(sinxcosx)# = #1/sinx-1/cosx# = #cscx-secx# 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 4128 views around the world You can reuse this answer Creative Commons License