What is cosh^2(x) + sinh^2(x)? Please explain.?

Answer 1

just go back to basics :
cosh(x) = (exp(x)+exp(-x))/2
sinh(x) = (exp(x)-exp(-x))/2

so cosh^2(x)+sinh2(x) =
(exp(2x) + 2 + exp(-2x))/4 + (exp(2x) - 2 + exp(-2x))/4 =
(exp(2x) + exp(-2x))/2 = cosh(2x)

in general cosh(ix) = cos(x) and sinh(ix) = i sin(x)
so cos(x) = cosh(ix) and sin(x) = -i sinh(ix)
and you can use this to mirror trig formulas
cos2x = cos^2(x)-sin^2(x) => cosh(2x)= cosh^2(x) + sinh^2(x)

Answer 2

1

Answer 3

cosh^2(x)+sinh^2(x)=cosh2x

cosh^2(x)-sinh^2(x)=1

this is bcoz it is a hyperbolic function
i'm very sure about my answer

normal trignometry function,cos^2+sin^2=1
but that is not same with hyperbolic functions

Answer 4

it is not 1 for hyperbolic functions!
cosh^2(x) - sinh^2(x) = 1
As far as your expression goes I am not sure what it equals but you might try writing hyperbolic functions in terms of e^x to see what it comes out to be.

Answer 5

cos^2(x) + sin^2(x) = 1
(This is a standard trig. identity.)

Therefore it is the same for the hyperbolic fuctions i.e. sinh and cosh.

Answer 6

cosh^2x-sinh^2x=1
where h is denoted by hiperbolic.
tihs is terignomecal equation.
then given equation is

cosh^2x+sinh^2x=cos2h^2x

Answer 7

cosh x = (1/2).(e^x + e^(-x))
sinh x = (1/2).(e^x - e ^(-x))

cosh²x = (1/4).[(e^(2x) + 2 + e^(-2x)]
sinh²x = (1/4).[e^(2x) - 2 + e^(-2x)]

Sum = (1/2). [e^(2x) + e^(- 2x)]
Sum = cosh 2x

Answer 8

An equation