Question

Show that

1+((e^x-e^-x)/2)^2 = ((e^x+e^-x)/2)^2

Can someone explain how does the 1st equation is equal to the 2nd one

Answer 1

LS = 1 + (e^(2x) - 2e^0 + e^(-2x) )/4

= (4 + e^(2x) - 2 + e^(-2x) )/4
= ( e^(2x) + 2e^0 + e^(-2x) )/4
= ( (e^x + e^-x)/2 )^2
= RS