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Let’s check out your problem:

y=(x)/(tan x)

y=xtan⁡x y=\frac{x}{\tan x}

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Full solution

Q. y=xtan⁡x y=\frac{x}{\tan x}
  1. Identify expression: Identify the expression for yy.y=xtan⁡(x)y = \frac{x}{\tan(x)}
  2. Simplify using identity: Simplify the expression using trigonometric identity. tan⁡(x)=sin⁡(x)cos⁡(x)\tan(x) = \frac{\sin(x)}{\cos(x)}, so y=x(sin⁡(x)/cos⁡(x))=x⋅(cos⁡(x)sin⁡(x))y = \frac{x}{(\sin(x) / \cos(x))} = x \cdot \left(\frac{\cos(x)}{\sin(x)}\right)
  3. Rewrite using cotangent: Rewrite the expression using cotangent.\newlinecot⁡(x)=cos⁡(x)sin⁡(x)\cot(x) = \frac{\cos(x)}{\sin(x)}, hence y=x⋅cot⁡(x)y = x \cdot \cot(x)

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