SOLUTION: find solutions of {{{sqrt(3)cos(x)+sin(x)=1}}}, on the interval[0,2{{{pi}}})

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Question 594183: find solutions of sqrt%283%29cos%28x%29%2Bsin%28x%29=1, on the interval[0,2pi)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283%29cos%28x%29%2Bsin%28x%29 = 1
Use the identity

A%2Acos%28theta%29+%2B+B%2Asin%28theta%29 = sqrt%28A%5E2%2BB%5E2%29%2Asin%28theta%2Balpha%29, where tan%28alpha%29=A%2FB and A+%3E+0, B+%3E+0

 A=sqrt%283%29, B+=+1, 

tan%28alpha%29=A%2FB
tan%28alpha%29=sqrt%283%29%2F1
alpha=%2260%B0%22=pi%2F3

sqrt%283%29cos%28x%29%2Bsin%28x%29 = 1
sqrt%28A%5E2%2BB%5E2%29%2Asin%28theta%2Balpha%29 = 1 
2sin%28theta%2Bpi%2F3%29 = 1
sin%28theta%2Bpi%2F3%29 = 1%2F2

theta%2Bpi%2F3 = pi%2F6, 5pi%2F6, 13pi%2F6, 17pi%2F6

theta = pi%2F6-pi%2F3, 5pi%2F6-pi%2F3, 13pi%2F3-pi%2F3, 17pi%2F6-pi%2F3

theta = pi%2F6-2pi%2F6, 5pi%2F6-2pi%2F6, 13pi%2F6-2pi%2F6, 17pi%2F6-2pi%2F6

theta = cross%28-pi%2F6%29, 3pi%2F6, 11pi%2F6, 15pi%2F6

theta =   pi%2F2, 11pi%2F6, cross%285pi%2F2%29

theta =   pi%2F2, 11pi%2F6

Edwin