# `4 sin x cos x=sqrt 3` Solve the equation.

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`4sinxcosx = sqrt3`

`2(2sinxcosx)=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