Solve 2\sin^3x+\sin3x+3\sin^2x\cos x+\cos^3x=0

compyac

compyac

Answered question

2022-04-22

Solve
2sin3x+sin3x+3sin2xcosx+cos3x=0

Answer & Explanation

Felicity Carter

Felicity Carter

Beginner2022-04-23Added 16 answers

Notice,
2sin3x+sin3x+3sin2xcosx+cos3x=0
2sin3x+3sinx4sin3x+3cosx(1cos2x)+cos3x=0
3sinx2sin3x+3cosx3cos3x+cos3x=0
3(cosx+sinx)2(cos3x+sin3x)=0
3(cosx+sinx)2(cosx+sinx)(cos2x+sin2xcosxsinx)=0
(cosx+sinx)(32(1cosxsinx))=0
cosx+sinx=012cosx+12sinx=0
cos(xπ4)=0xπ4=(2n+1)π2
x=(4n+3)π4
or
32(1cosxsinx)=02sinxcosx=1
x=nππ4=(4n1)π4

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?