How do you solve ${csc}^{2} x - 2 {cot}^{2} x = 0$ $csc^2x-2cot^2x=0$ ?

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Answer 1 · 2016-10-05T13:47:43

$\frac{1}{{sin}^{2} x} - \frac{2 {cos}^{2} x}{{sin}^{2} x} = 0$ $1/sin^2x - (2cos^2x)/sin^2x = 0$

$\frac{1 - 2 {cos}^{2} x}{{sin}^{2} x} = 0$ $(1 - 2cos^2x)/sin^2x = 0$

${csc}^{2} x (1 - 2 {cos}^{2} x) = 0$ $csc^2x(1 - 2cos^2x) = 0$

${csc}^{2} x = 0 A N D cos x = \pm \frac{1}{\sqrt{2}}$ $csc^2x = 0" "AND" "cosx = +-1/sqrt(2)$

$x = 45˚, 135˚, 225˚, 315˚$

Hopefully this helps!

How do you solve csc^2x-2cot^2x=0csc2x−2cot2x=0csc^2x-2cot^2x=0?