Question

please help to prove
cosh 3x = 4 cosh^3 x - 3 cosh x

Answer 1

do u know the proof for cos3x=4cos^3 x - 3 cos x?

Answer 2

cosh(a + b) = coshacoshb - sinhasinhb
sinh(a + b) = sinhacoshb + coshasinhb
sinh^2a + cosh^2a = 1
Consider the left hand side:
cosh3x
= cosh(2x + x)
= cosh2xcoshx - sinh2xsinhx
= cosh(x + x)coshx - sinh(x + x)sinhx
= (coshxcoshx - sinhxsinhx)coshx - (sinhxcoshx + coshxsinhx)sinhx
= (cosh^2x - sinh^2x)coshx - (2sinhxcoshx)sinhx
= (cosh^2x - (1 - cosh^2x))coshx - 2sinh^2xcoshx
= (cosh^2x - 1 + cosh^2x)coshx - 2(1 - cosh^2x)coshx
= (2cosh^2x - 1)coshx - 2(coshx - cosh^3x)
= 2cosh^3x - coshx - 2coshx + 2cosh^3x
= 4cosh^3x - 3coshx

Answer 3

i think it will be fine....

Answer 4

thanks :D this really helpful

Answer 5

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