How do you verify #(2 + cos^2 x)(1+ tan^2 x)= 3 + 2tan^2 x#? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub Oct 7, 2016 see below Explanation: #(2+cos^2x)(1+tan^2x)=3+2 tan^2x# Left Side :#=(2+cos^2x)(1+tan^2x)# #=2+2tan^2x+cos^2x+cos^2xtan^2x# #=2+2tan^2x+cos^2x+cos^2x sin^2x/cos^2x# #=2+2tan^2x+cos^2x+cancel(cos^2x) sin^2x/cancel(cos^2x)# #=2+2tan^2x+cos^2x+sin^2x# #=2+2tan^2x+1# #=3+2tan^2x# #:.=#Right Side 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 1818 views around the world You can reuse this answer Creative Commons License