Question Number 105112 by bemath last updated on 26/Jul/20

2(√3) sin ^2 (x+((3π)/2)) + sin 2x = 0   0≤x≤2π

Answered by john santu last updated on 28/Jul/20

⇔ 2(√3) cos ^2 (x)+ sin (2x) = 0  2cos (x) {(√3) cos x+sin x } = 0   { ((cos x = 0 →x = (π/2)+2kπ)),((tan x = −(√3) = tan ((2π)/3) →x=((2π)/3)+kπ)) :}   { ((x = (π/2))),((x = ((2π)/3) ; ((5π)/3))) :}   (JS ♠★)

Answered by Dwaipayan Shikari last updated on 26/Jul/20

2(√3)cos^2 x+2sinxcosx=0  4cosx(((√3)/2)cosx+(1/2)sinx)=0  4cosx=0  x=(4k+1)(π/2)......(a)  or(((√3)/2)cosx+(1/2)sinx)=0  sin((π/3)+x)=0  (π/3)+x=kπ  x=kπ±(π/3)   { ((x=(π/2))),((x=((2π)/3),((5π)/3))) :}