How do you solve sin3x=cos3x*tan3x for x in the interval [0,2pi)?

1 Answer
Alan P.
Apr 26, 2016

The given equation is true for all values in the range [0,2pi)

Explanation:

You could (temporarily) replace 3x with theta
so the given equation would look like:
color(white)("XXX")sin(theta)=cos(theta)*tan(theta)

But we know that tan(theta)=(sin(theta))/(cos(theta))

So we have that the given equation is equivalent to
color(white)("XXX")sin(theta)=(cancel(cos(theta)))/color(white)("X")*(sin(theta))/(cancel(cos(theta)))

Which is true for all values of theta and therefore true for all values of x.

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
2068 views around the world
You can reuse this answer
Creative Commons License