How do you prove that #(1 + tan theta)[1 + tan(1/4 pi - theta)] = 2#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Massimiliano Feb 17, 2015 Remembering that: #tan(alpha-beta)=(tanalpha-tanbeta)/(1+tanalphatanbeta)#, and #tan(pi/4)=1#, than: #(1+tantheta)(1+(tan(pi/4)-tantheta)/(1+tan(pi/4)tantheta))=2rArr# #(1+tantheta)(1+(1-tantheta)/(1+tantheta))=2rArr# #(1+tantheta)((1+tantheta+1-tantheta)/(1+tantheta))=2rArr# #2=2#, with simply calculations. 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 7075 views around the world You can reuse this answer Creative Commons License