How do you solve $2sin(x+pi/3)=tan(pi/3)$ ?

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Answer 1 · 2016-07-18T09:34:43

$x=npi+((-1)^n-1)(pi/3), n = 0, +-1, +-2, +-3, ..$ and this includes 0 for n = 0.

Inversely,

$x+pi/3=sin^(-1)((1/2)tan (pi/3)$

$=sin^(-1)(1/2sqrt 3)$ = pi/3#, as principal value and

$=npi+(-1)^npi/3, n = 0, +-1, +-2, +-3, ..$ , as general value. So,

$x=.npi+((-1)^n-1)(pi/3), n = 0, +-1, +-2, +-3, ..$ and this includes 0 for n = 0.

How do you solve 2sin(x+pi/3)=tan(pi/3)2sin(x+pi/3)=tan(pi/3)?