Question #7392e

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Answer 1 · 2017-03-27T00:40:23

$3cscx-2sqrt3=0$

Add $2sqrt3$ to both sides
$3cscxcancel(-2sqrt3)cancel(+2sqrt3)=cancel(0+)2sqrt3$
$3cscx=2sqrt3$

Divide both sides by $3$
$(cancel3cscx)/cancel3=(2sqrt3)/3$
$cscx=(2sqrt3)/3$

Replace $cscx$ with $1/sinx$ and $sqrt3/3$ with $1/sqrt3$
$1/sinx=2/sqrt3$

Raise both sides to the power of $"-"1$ and simplify
$(1/sinx)^("-"1)=(2/sqrt3)^("-"1)$
$sinx=sqrt3/2$

Use knowledge of special angles (or a calculator if you don't need an exact answer)
$x=pi/3$

Realize that $sin(pi-theta)=sin(theta)$
$x=pi/3,(2pi)/3$

Since $x$ is unbounded and $f(x+2npi)=f(x)$ when $f(theta)$ is a trig function and $ninZZ$

${x:x=pi/3+2npi,(2pi)/3+2npi;ninZZ}$