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Math Help - Product of Tangents

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    Product of Tangents

    How do i evaluate (tan 12)(tan 48)(tan 54)(tan 72) without using a calculator?
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    re: Product of Tangents

    Quote Originally Posted by hooke View Post
    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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