Question #5c457 Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer P dilip_k Apr 9, 2017 #LHS=(sinx + cosx) (secx+ cosecx)# #=(sinx + cosx) (1/cosx+ 1/sinx)# #=(sinx + cosx) ((sinx+cosx)/(cosxsinx))# #= ((sinx+cosx)^2/(cosxsinx))# #= ((sin^2x+cos^2x+2sinxcosx)/(cosxsinx))# #= (1+2sinxcosx)/(cosxsinx)# #= (1/(cosxsinx)+(2sinxcosx)/(cosxsinx))# #=secxcosecx+2# # = 2 + secx cosecx=RHS# So this is not an equation but an identity. 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 1031 views around the world You can reuse this answer Creative Commons License