Exercise
$\cos\left(x\right)=\frac{1}{\sqrt{1+\cot^2\left(x\right)}}$
Step-by-step Solution
Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation cos(x)=1/((1+cot(x)^2)^(1/2)). Apply the trigonometric identity: 1+\cot\left(\theta \right)^2=\csc\left(\theta \right)^2. Cancel exponents 2 and 1. Apply the trigonometric identity: \frac{1}{\csc\left(\theta \right)}=\sin\left(\theta \right). Divide both sides of the equation by \cos.
Solve the trigonometric equation cos(x)=1/((1+cot(x)^2)^(1/2))
Final answer to the exercise
$x=\frac{1}{4}\pi+\pi n,\:x=\frac{5}{4}\pi+\pi n\:,\:\:n\in\Z$