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

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justaguide eNotes educator| Certified Educator

The equation `sin x cos x = sqrt 3 / 4` has to be solved.

`sin x cos x = sqrt 3 / 4`

=> `2*sin x*cos x = sqrt 3/2`

=> `sin (2x) = sqrt 3/2`

=> 2x = 60 and 2x = 120

=> x = 30 and x = 60 degrees

The general solution of the equation is 30 + n*360 degrees and 60 + n*360 degrees.

oldnick | Student

`sinxcosx= 1/2(sin(x+x)-sin(x-x))=1/2sin2x```

so:

`1/2sin2x=sqrt(3)/4i`   `sin2x=sqrt(3)/2`     `2x=pi/3`   `2x=2/3pi`

 

`x=pi(1/3+2k)`   `x=2pi(1/3+k)`

 

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