Question

(cot theta - sin theta) (sec theta - cos theta) =1/tan theta+cot theta
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Answer 1

Answer:

Step-by-step explanation:

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Answer 2

LHS

$(cosec \theta - sin \theta)(sec \theta - cos \theta) \\ \\ = ( \frac{1 - {sin \theta}^{2} }{sin \theta} )( \frac{1 - {cos}^{2} \theta }{cos \theta} ) \\ \\ = \frac{ {sin}^{2} \theta {cos}^{2} \theta }{sin \theta cos \theta} \\ \\ = sin \theta cos \theta$

RHS

$\frac{1}{tan \theta + cot \theta} \\ \\ = \frac{1}{ \frac{ {sin}^{2} \theta + {cos}^{2} \theta}{sin \theta cos \theta} } \\ \\ = sin \theta cos \theta$

LHS=RHS