How does one solve \sin x-\sqrt{3} \cos x=1 I thought this one up, but I am not sure how t

Laney Spears

Laney Spears

Answered question

2022-01-29

How does one solve sinx3cosx=1
I thought this one up, but I am not sure how to solve it. Here is my attempt:
sinx3cosx=1
(sinx3cosx)2=1
sin2x23sinxcosx+3cos2x=1
123sinxcosx+2cos2x=1
2cos2x23sinxcosx=0
2cosx(cosx3sinx)=0
2cosx=0x{π2(2n1):nZ}
But how do I solve
cosx3sinx=0

Answer & Explanation

chukizosv

chukizosv

Beginner2022-01-30Added 8 answers

Hint: at the very beginning divide both sides by 2 and use the formula for the sin of difference of 2 arguments
vasselefa

vasselefa

Beginner2022-01-31Added 9 answers

Hint :
cosx3sinx=0sinxcosx=33tanx=33
Note : You can divide by cosx since if the case was cosx=0 it would be sinx=±1 and thus the equation would yield ±3±0, thus no problems in the final solution, as the cos zeros are no part of it.

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?