How do you prove cosh(2x) = cosh²x + sinh²x? Trigonometry Trigonometric Identities and Equations Proving Identities 1 Answer Bdub May 5, 2016 see below Explanation: Use formula: cosh x=(e^x+e^-x)/2 and sinh x = (e^x-e^-x)/2 Right side:=cosh^2x+sinh^2x =((e^x+e^-x)/2)^2 +((e^x-e^-x)/2)^2 =(e^(2x)+2+e^(-2x))/4 + (e^(2x)-2+e^(-2x))/4 =(e^(2x)+2+e^(-2x)+e^(2x)-2+e^(-2x))/4 =(2e^(2x)+2e^(-2x))/4 =(2(e^(2x)+e^(-2x)))/4 =(e^(2x)+e^(-2x))/2 =cosh (2x) = Left 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 51576 views around the world You can reuse this answer Creative Commons License