How do you prove cosh (2x) = cosh²x + sinh²x? | Socratic
2016年5月5日 · see below 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 ...
What is cosh(ln(x))? | Socratic
2015年11月7日 · cosh(z) = ez + e−z 2 So: cosh(ln(x)) = eln(x) +e−ln(x) 2 = x + 1 x 2 = x2 + 1 2x
How do you prove Arc cosh(x) = ln(x + (x^2 - 1)^(1/2))? | Socratic
2016年5月4日 · see below Let y=cosh^-1x then by definition x=cosh y = (e^y+e^-y)/2 2x=e^y+e^-y e^y-2x+e^-y=0 e^y-2x+1/e^y=0 e^ (2y)-2xe^y+1=0 Let u=e^y then we have u^2-2xu+1=0 ...
Prove that Cosh (2x)=2cos2x-1? - Socratic
2018年3月6日 · See the proof below I am going to prove the following cosh2x=2cosh^2x-1 By the definition of hyperbolic functions cosh (2x)= (e^ (2x)+e^ (-2x))/2 coshx= (e^x+e^-x ...
How do you show that cosh^2 x - sinh^2 x = 1 ? | Socratic
2017年10月15日 · See explanation... >cosh x = 1/2 (e^x+e^ (-x)) sinh x = 1/2 (e^x-e^ (-x)) So: cosh^2 x - sinh^2 x = 1/4 ( (e^x+e^ (-x))^2- (e^x-e^ (-x))^2) color (white) (cosh^2 x ...
From cosh2A = 1+2 (sinh^2)A, how do you prove that (sinh^4)A
2017年2月7日 · From cosh 2A = 1 + 2(sinh2)A, how do you prove that (sinh4)A + (cosh4)A = cosh 4A + 3 4 and also (cosh4)A − (sinh4)A = cosh 2A?
How do you prove Cosh(A+B) = CoshA*CoshB+SinhB*SinhA?
2016年5月3日 · See below Use the definition of Hyperbolic Functions for cosh x cosh x = (e^x + e^-x)/2 and sinh x= (e^x-e^-x)/2 cosh (A+B)=coshAcoshB+sinhAsinhB Right Side: = [ (e^A ...
Evaluate the integral? int ln tanh (x/2)/cosh^2x dx | Socratic
2017年7月24日 · I got = tanh(x)ln(tanh(x/2)) - 2arctan(tanh(x/2)) + C, " "x > 0 DISCLAIMER: VERY LONG ANSWER! Well, I don't work with hyperbolics much, but I do know that: the derivative of tanh(x) is still sech^2(x). we still have cosh(x) = 1/(sech(x)). we however, have that -sinh^2(x) + cosh^2(x) = 1, so that tanh^2(x) + sech^2(x) = 1 and 1 + csch^2(x) = coth^2(x). So, we have: = int sech^2(x)ln (tanh(x/2 ...
How do you find the power series for f (x)=cosh (x^2) and
2018年4月16日 · How do you find the power series for f (x) = cosh(x2) and determine its radius of convergence?
How do you find the antiderivative of int sqrt(x^2-1) dx? | Socratic
2017年3月5日 · = 1/2 x sqrt(x^2 - 1) - 1/2 cosh^(-1) (x) + C When you say you want the "anti-derivative" of int sqrt(x^2-1) dx, I am assuming you mean you want the "anti-derivative" that is int sqrt(x^2-1) dx. Otherwise you are looking for: int ( int sqrt(x^2-1) dx) \\ dx. For int sqrt(x^2-1) \\ dx, there is a convenient hyperbolic relationship: cosh^2 z - sin^2 z = 1 If we let x …