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

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lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

`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`

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sampath729 | Student, Undergraduate | eNotes Newbie

Posted on

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  

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