How do I solve this equation \(\displaystyle{\mathbb{{{R}}}}\):

Aiyana Ayers

Aiyana Ayers

Answered question

2022-04-16

How do I solve this equation R:
3sin3x+2cos3x=2sinx+cosx

Answer & Explanation

coesarfaujs3t

coesarfaujs3t

Beginner2022-04-17Added 11 answers

One possible way is to rewrite the equality as
3sin3(x)2sin(x)=2cos3(x)+cos(x)
WARNING: The following step may introduce extra solutions which will need to be checked at the end.
Now, square both sides.
9sin6(x)12sin4(x)+4sin2(x)=4cos6(x)4cos4(x)+cos2(x)
Using the trig identity cos2(x)=1sin2(x), you can rewrite this entirely in terms of sin2(x). When I did this on scratch paper, I got
13sin(x)620sin(x)4+9sin(x)21.
Finally, let y=sin2(x) and you have the cubic equation
13y220y2+9y1
to solve.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?