Question 1192245: Find the expression for tan3x in term of tan(x) only
tan3x = (sin3x/cos3x)
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! duplicate
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Picking an angle and checking that the formula is correct does NOT necessarily mean it is correct for all angles.
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RE: the formula:
If it is not correct for any angle tested, it is not valid.
It it is correct for any angle(s), it might be valid, might not be.
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As an example:
Prove sin(x) = cos(x)
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Let x = 45 degs
QED
sin(x) <> cos(x) in general.
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It's possible the other tutor knew that formula from memory, but not likely.
He probably looked it up, as you could have done.
There are WAAAAYYYY too many formulas for anyone to remember, IMO.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website!
3 * tan(x) - tan^3(x)
tan(3x) = ----------------------------------
(1 - 3 * tan^2(x)
you can prove that it's true by taking any angle and multiplying it by 3 and then taking the tangent of.
then you use the formula and you should get the same answer.
for example, i chose 92 degrees.
3 * 92 degrees = 276 degrees.
tan(276) = -9.514364453.
using the formula, i get:
3 * tan(92) - tan^3(92)
tan(3x) = ---------------------------------- = -9.514364454
(1 - 3 * tan^2(92)
they're the same, confirming the formula is correct.
that little discrepancy between the numbers at the end (4 versus 3) is due to internal rounding differences in the calculation of one formula versus the other.
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