How do i evaluate (tan 12)(tan 48)(tan 54)(tan 72) without using a calculator?
$\displaystyle (tan 12)(tan 48)(tan 54)(tan 72)=\frac{sin(12)}{cos(12)}\frac{sin(48)}{cos(48)} \frac{sin(54)}{cos(54)}\frac{sin(72)}{cos(72)} $
Now, use the following identities:
1) $\displaystyle sin(x)sin(y)=\frac{1}{2}(cos(x-y)-cos(x+y)) $
2) $\displaystyle cos(x)cos(y)=\frac{1}{2}(cos(x+y)+cos(x-y)) $