Exercise
$2\sin^{4}x-3\sin^{2}x+1=0$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation 2sin(x)^4-3sin(x)^2+1=0. Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side. Factor the polynomial 2\sin\left(x\right)^4-3\sin\left(x\right)^2 by it's greatest common factor (GCF): \sin\left(x\right)^2. Applying the trigonometric identity: \sin\left(\theta \right)^2 = 1-\cos\left(\theta \right)^2. Multiplying polynomials 1-\cos\left(x\right)^2 and 2\sin\left(x\right)^2-3.
Solve the trigonometric equation 2sin(x)^4-3sin(x)^2+1=0
Final answer to the exercise
$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n,\:x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n\:,\:\:n\in\Z$