Question

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

Answer 1

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

Explanation:

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.