How do you show that #2cos(2x)cosh(x) = cosh(3x) + cosh(x)# ?
1 Answer
Dec 17, 2017
See explanation...
Explanation:
Note that:
#cosh(x) = 1/2(e^x+e^(-x))#
So:
#2 cosh(2x)cosh(x) = 2 * 1/2(e^(2x)+e^(-2x)) * 1/2(e^x+e^(-x))#
#color(white)(2 cosh(2x)cosh(x)) = 1/2(e^(2x)e^x+e^(-2x)e^(-x)+e^(2x)e^(-x)+e^(-2x)e^x)#
#color(white)(2 cosh(2x)cosh(x)) = 1/2(e^(3x)+e^(-3x)+e^x+e^(-x))#
#color(white)(2 cosh(2x)cosh(x)) = 1/2(e^(3x)+e^(-3x))+1/2(e^x+e^(-x))#
#color(white)(2 cosh(2x)cosh(x)) = cosh(3x)+cosh(x)#
