Exercise
$cot^2\left(x\right)-3csc+3=0$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation cot(x)^2-3csc(x)+3=0. Applying the trigonometric identity: \cot\left(\theta \right)^2 = \csc\left(\theta \right)^2-1. We can try to factor the expression \csc\left(x\right)^2+2-3\csc\left(x\right) by applying the following substitution. Substituting in the polynomial, the expression results in. Factor the trinomial u^2+2-3u finding two numbers that multiply to form 2 and added form -3.
Solve the trigonometric equation cot(x)^2-3csc(x)+3=0
Final answer to the exercise
$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n\:,\:\:n\in\Z$