SOLUTION: Prove the formula tan3@ = 3tan@ - tan^3@ / 1 - 3tan^2@.
Hence solve the equation tan3@ = 0
If 0≤@≤360
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Question 1202935: Prove the formula tan3@ = 3tan@ - tan^3@ / 1 - 3tan^2@.
Hence solve the equation tan3@ = 0
If 0≤@≤360
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
One of the many trig identities is
Let's plug in A = x and B = x
this will be useful in substitution steps later on.
Go back to
Let's plug in
A = x
B = 2x
to get the following
This is one large fraction with
numerator = tan(x)+tan(2x)
denominator = 1-tan(x)*tan(2x)
In other words,
where
and
Let's apply a substitution in the numerator
Apply that same substitution with the denominator.
------------------------------------
Recall that this identity
is of the form
where
and
but we found these equivalent forms
and
The 2nd versions of P and Q involve the denominator .
Those expressions cancel when dividing.
Therefore,
------------------------------------
For the next part of the problem, here are a few hints:
I'll let you take over from here.
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