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What is $\tan15\cdot \tan 30 \cdot \tan 45 \cdot \tan 60 \cdot \tan 75$ equal to (in degrees)?

Here is how I tried to solve it:

I assumed $x = \tan 15 (x= 0.27)$, so I rewrote it as:

$x\cdot 2x \cdot 3x \cdot 4x \cdot 5x = 120x^5$

$0.27^5 = 0.001323$

$120 \cdot 0.001323 = 0.16$

But Google Calculator gives me $-1.19576279$

What is the right way to calculate this trig expression?

  • 2
    Why are you thinking that the tangent values increase linearly?2012-05-18
  • 2
    Tangent is not linear! P.S. Google Calculator computed the result using radians, not degrees.2012-05-18

4 Answers 4