Exercise
$sen\left(2x\right)-2cos\left(x\right)+sen\left(x\right)-1=0$
Step-by-step Solution
Learn how to solve simplification of algebraic expressions problems step by step online. Solve the trigonometric equation sin(2x)-2cos(x)sin(x)+-1=0. Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right). Factor 2\sin\left(x\right)\cos\left(x\right)-2\cos\left(x\right)+\sin\left(x\right)-1 by the greatest common divisor 2. Factoring by \sin\left(x\right)-1. Break the equation in 2 factors and set each factor equal to zero, to obtain simpler equations.
Solve the trigonometric equation sin(2x)-2cos(x)sin(x)+-1=0
Final answer to the exercise
$x=\frac{1}{2}\pi+2\pi n\:,\:\:n\in\Z$