How do you solve the equation $3 {csc}^{2} x = 4$ $3csc^2x=4$ ?

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Answer 1 · 2017-03-24T21:40:40

see below

$3 {csc}^{2} x = 4$ $3 csc^2 x = 4$

$\frac{3}{{sin}^{2} x} = 4$ $3/sin^2 x=4$

$3 = 4 {sin}^{2} x$ $3=4sin^2 x$

$\frac{3}{4} = {sin}^{2} x$ $3/4 = sin^2 x$

$\pm \frac{\sqrt{3}}{2} = sin x$ $+- sqrt 3/2 = sinx$

$x = {sin}^{- 1} (\pm \frac{\sqrt{3}}{2})$ $x=sin^-1 (+- sqrt 3/2)$

$x = \pm \frac{π}{3} + 2 π n, \pm \frac{2 π}{3} + 2 π n$ $x=+- pi/3+2pin, +-(2pi)/3 +2pin$

$S = {\pm \frac{π}{3} + 2 π n, \pm \frac{2 π}{3} + 2 π n}$ $S={+- pi/3+2pin, +-(2pi)/3 +2pin}$

How do you solve the equation 3csc^2x=43csc2x=43csc^2x=4?