!!help me please log and trigonometry?

Question

1) 6log(x-y) = logx^3 +logy^3
find sum of all x/y

2)cos20cos40cos80 need fasten formula (not simply)

3)sin40sin80sin160 need fasten formula (not simply)

thank very much ^-^

Puggy , and All top please help..

Answer 1

1.6log(x-y) = logx^3 +logy^3
= 3log x + 3 log y
2 log (x-y) = log x + log y
= log (x*y)
log (x-y)^2 = log (x*y)
10^(log(x-y)^2) = 10^(log(xy) <--- to rid of the log
(x-y)^2 = xy
x^2 +y^2 - 2xy = xy
x^2 + y ^2 = 3xy

Now you can do the rest.