Exercise
$\frac{1}{\cos\left(x\right)}=sec\left(x\right)-tan\left(x\right)sin\left(x\right)$
Step-by-step Solution
Learn how to solve integrals of rational functions problems step by step online. Solve the trigonometric equation 1/cos(x)=sec(x)-tan(x)sin(x). Applying the trigonometric identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. 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. Cancel like terms \sec\left(x\right) and -\sec\left(x\right). Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}.
Solve the trigonometric equation 1/cos(x)=sec(x)-tan(x)sin(x)
Final answer to the exercise
$x=0+2\pi n,\:x=2\pi+2\pi n\:,\:\:n\in\Z$