Proving Hyperbolic Identities (5 examples)

We will prove 5 hyperbolic identities. We will mainly use sinh(x)=(e^x-e^(-x))/2 and cosh(x)=(e^x+e^(-x))/2 to show these results. Subscribe for more precalculus & calculus tutorials 👉 https://bit.ly/just_calc 0:00 sinh^2(x)=-1/2+1/2cosh(2x) 2:51 sinh(2x)=2sinh(x)cosh(x) 6:02 sinh^2(x)+cosh^2(x)=cosh(2x) 9:14 tanh(ln(x))=(x^2-1)/(x^2+1) 11:44 1-tanh^2(x)=sech^2(x) --------------------------------------------------------- If you find this channel helpful and want to support it, then you can join the channel membership and have your name in the video descriptions: 👉https://bit.ly/joinjustcalculus buy a math shirt or a hoodie (10% off with the code "WELCOME10"): 👉 https://bit.ly/bprp_merch "Just Calculus" is dedicated to helping students who are taking precalculus, AP calculus, GCSE, A-Level, year 12 maths, college calculus, or high school calculus. Topics include functions, limits, indeterminate forms, derivatives, and their applications, integration techniques and their applications, separable differential equations, sequences, series convergence test, power series a lot more. Feel free to leave calculus questions in the comment section and subscribe for future videos 👉 https://bit.ly/just_calc --------------------------------------------------------- Best wishes to you, #justcalculus