Exercise
$\cos\left(2x\right)=3-5\sin$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation cos(2x)=3-5sin(x). Move everything to the left hand side of the equation. Applying an identity of double-angle cosine: \cos\left(2\theta\right)=1-2\sin\left(\theta\right)^2. We can try to factor the expression -2-2\sin\left(x\right)^2+5\sin\left(x\right) by applying the following substitution. Substituting in the polynomial, the expression results in.
Solve the trigonometric equation cos(2x)=3-5sin(x)
Final answer to the exercise
$x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n\:,\:\:n\in\Z$