`4sinxcosx = sqrt3`
Replace `2sinxcosx` with `sin (2x)` . Note that base on the double angle identity `sin(2x) = 2sinxcosx` .
`2 sin (2x) = sqrt 3`
`sin 2x = sqrt3/2`
Refer to Unit Circle Chart to determine the angle `2x` . Then, solve for x.
`2x = pi/3 ` and `2x = (2pi)/3`
`x = pi/6` `x = pi/3`
Since there is no indicated interval for angle x, the general solutions for x are:
`x_1 = pi/6 + 2pik` and `x_ 2 = pi/3 + 2pik`
a*b is positive if 1)a is positive and b is positive
1)a is negative and b is negative
so x must lie in first or third quadrant
from equation 2sin2x = sqrt(3)
=> 2x = 2nPI+60 or 2nPI+120
=> x = nPI+30 or nPI+60