Exercise
$\cos\left(\arctan\left(\frac{x}{5}\right)\right)$
Step-by-step Solution
Learn how to solve equivalent expressions problems step by step online. Simplify the expression cos(arctan(x/5)). Simplify \cos\left(\arctan\left(\frac{x}{5}\right)\right) as \frac{1}{\sqrt{\left(\frac{x}{5}\right)^2+1}}. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Calculate the power 5^2. Combine \frac{x^2}{25}+1 in a single fraction.
Simplify the expression cos(arctan(x/5))
Final answer to the exercise
$\frac{5}{\sqrt{x^2+25}}$