Exercise
$5\sin\left(x\right)\cos\left(x\right)+4\cos\left(x\right)=0$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation 5sin(x)cos(x)+4cos(x)=0. Simplify 5\sin\left(x\right)\cos\left(x\right) using the trigonometric identity: \sin(2x)=2\sin(x)\cos(x). We need to isolate the dependent variable x, we can do that by simultaneously subtracting 4\cos\left(x\right) from both sides of the equation. Multiply both sides of the equation by 2. Simplify, dividing both sides of the equality by .
Solve the trigonometric equation 5sin(x)cos(x)+4cos(x)=0
Final answer to the exercise
$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n\:,\:\:n\in\Z$