Help me with double angle formula?

E

evergreens

New member
it states that cosh^2(x) = 1/2(1 + cosh(2x)

so.....cosh^2 (2x) = 1/2(1 + cosh(4x)......? Is this right?

and another question: Is cos^2 (x) the same thing as (cos(x))^2 ?
 
Here,
cosh^2(x) = 1/2(1 + cosh(2x)

L.H.S. = cosh^2(x) = (coshx)^2 = [(e^x+e^-x)/2]^2 =

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

= 1/2(1 + cosh(2x) = R.H.S. >=========================< Q . E . D.

ALSO,
cosh^2 (2x) = 1/2(1 + cosh(4x) .... you are correct.

Hence,
cos^2x = (cosx)^2 ... Again you are correct >===========, ANSWER
 
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