Exercise
$\tan\left(x\right)=\frac{1}{\sin\left(x\right)\cdot\cos\left(x\right)}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the trigonometric equation tan(x)=1/(sin(x)cos(x)). Simplify \sin\left(x\right)\cos\left(x\right) using the trigonometric identity: \sin(2x)=2\sin(x)\cos(x). Divide fractions \frac{1}{\frac{\sin\left(2x\right)}{2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Multiply both sides of the equation by \sin\left(2x\right). Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right).
Solve the trigonometric equation tan(x)=1/(sin(x)cos(x))
Final answer to the exercise
$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n\:,\:\:n\in\Z$