Question

Tolong jawab no 5 Kak...please

Answer 1

Set  
a^x = k
a^(-x)  = l

a^y = m
a^(-y) = n

f(x) . f(y) + g(x) . g(y) =
= 1/2 (k+l) . 1/2 (m+n) + 1/2 (k-l) . 1/2 (m-n)
= 1/4 (k+l)(m+n) + 1/4 (k-l)(m-n)
= 1/4 [ km + kn + lm+ ln + km - kn - lm + ln  ]
= 1/4 ( 2 km + 2 ln )
= 1/2 (km + ln)
= 1/2 ( a^x. a^y + a^-x . a^-y)
= 1/2 ( a^(x+y) + a^-(x+y)) = f(x + y)