Question #df763 Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Narad T. Dec 12, 2016 The answer is #=1# Explanation: We use, #tanx=sinx/cosx# Then, #cosx+sinx=sqrt2cosx# Divide by #cosx# #1+tanx=sqrt2# #tanx=sqrt2-1# #tan^2x+2tanx=(sqrt2-1)^2+2(sqrt2-1)# #=2+1-2sqrt2+2sqrt2-2# #=1# 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 1175 views around the world You can reuse this answer Creative Commons License