Question

(1+tan theta+cot theta)(sin theta-cos theta)=​

Answer 1

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Answer 2

$(1 + tan \theta + cot \theta)(sin \theta - cos \theta) \\ \\ = (1 + \frac{sin \theta}{cos \theta } + \frac{cos \theta}{sin \theta} )(sin \theta - cos \theta) \\ \\ = ( \frac{sin \theta cos \theta + 1}{sin \theta cos \theta} )(sin \theta - cos \theta)$

$= \frac{ {sin}^{3} \theta - {cos}^{3} \theta}{sin \theta cos \theta} \\ \\ = \frac{ {sin}^{2} \theta }{cos \theta} - \frac{ {cos}^{2} \theta}{sin \theta}$

$= sin \theta tan \theta - cos \theta cot \theta$