Product of Tangents

**hooke** · June 14th 2011, 05:36 AM

How do i evaluate (tan 12)(tan 48)(tan 54)(tan 72) without using a calculator?

**Also sprach Zarathustra** · June 14th 2011, 09:43 AM

Originally Posted by hooke

How do i evaluate (tan 12)(tan 48)(tan 54)(tan 72) without using a calculator?

$(tan 12)(tan 48)(tan 54)(tan 72)=\frac{sin(12)}{cos(12)}\frac{sin(48)}{cos(48)} \frac{sin(54)}{cos(54)}\frac{sin(72)}{cos(72)}$

Now, use the following identities:

1) $sin(x)sin(y)=\frac{1}{2}(cos(x-y)-cos(x+y))$

2) $cos(x)cos(y)=\frac{1}{2}(cos(x+y)+cos(x-y))$

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