Complete the identity. \( \tan x(\cot x-\cos x)=? \)

Calculate or simplify the expression \( \tan(x)(\cot(x)-\cos(x)) \). Simplify the expression by following steps: - step0: Solution: \(\tan\left(x\right)\left(\cot\left(x\right)-\cos\left(x\right)\right)\) - step1: Transform the expression: \(\frac{\sin\left(x\right)}{\cos\left(x\right)}\times \left(\cot\left(x\right)-\cos\left(x\right)\right)\) - step2: Transform the expression: \(\frac{\sin\left(x\right)}{\cos\left(x\right)}\times \frac{\cos\left(x\right)-\cos\left(x\right)\sin\left(x\right)}{\sin\left(x\right)}\) - step3: Reduce the fraction: \(\frac{1}{\cos\left(x\right)}\times \left(\cos\left(x\right)-\cos\left(x\right)\sin\left(x\right)\right)\) - step4: Rewrite the expression: \(\frac{1}{\cos\left(x\right)}\times \cos\left(x\right)\left(1-\sin\left(x\right)\right)\) - step5: Reduce the fraction: \(1\times \left(1-\sin\left(x\right)\right)\) - step6: Multiply the terms: \(1-\sin\left(x\right)\) The completed identity is \( \tan x(\cot x-\cos x) = 1 - \sin x \).