How does one solve sin⁡x−3cos⁡x=1 I thought this one up, but I am not sure...

Laney Spears

Laney Spears

Answered

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

Expert

2022-01-30Added 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

Expert

2022-01-31Added 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.

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