ab*Arctan((acotx)/(b))

Rewrite using identities: Step 1: Rewrite the expression using trigonometric identities. Arctan and cotangent are inverse functions, so acot(x) can be rewritten as 1/tan(x). Thus, the expression becomes abArctan((1/tan(x))/b).Simplify inside Arctan: Step 2: Simplify the expression inside Arctan. (1/tan(x))/b simplifies to 1/(b*tan(x)). Therefore, the expression now is abArctan(1/(b*tan(x))).Apply Arctan property: Step 3: Apply the property of Arctan. Arctan(1/y) = cot(y) for y = b*tan(x). Therefore, abArctan(1/(b*tan(x))) simplifies to abcot(b*tan(x)).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify the expression : $ab*\arctan\left(\frac{\cot x}{b}\right)$

View step-by-step help

Home

Math Problems

Precalculus

Evaluate rational exponents

Full solution

Q. Simplify the expression :

ab*\arctan\left(\frac{\cot x}{b}\right)

Rewrite using identities: Step $1$ : Rewrite the expression using trigonometric identities. $\newline$ Arctan and cotangent are inverse functions, so $\text{acot}(x)$ can be rewritten as $\frac{1}{\tan(x)}$ . Thus, the expression becomes $ab\text{Arctan}\left(\frac{\frac{1}{\tan(x)}}{b}\right)$ .
Simplify inside Arctan: Step $2$ : Simplify the expression inside Arctan. $\newline$ $(\frac{1}{\tan(x)})/b$ simplifies to $\frac{1}{b\tan(x)}$ . Therefore, the expression now is $ab\text{Arctan}(\frac{1}{b\tan(x)})$ .
Apply Arctan property: Step $3$ : Apply the property of Arctan. $\text{Arctan}(\frac{1}{y}) = \cot(y)$ for $y = b\tan(x)$ . Therefore, $ab\text{Arctan}(\frac{1}{(b\tan(x))})$ simplifies to $ab\cot(b\tan(x))$ .