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