Question

2 sin theta . cos theta - cos theta / 1 -sin theta plus sin square - cos square =cot theta​

Answer 1

Please see the attachment

Answer 2

$LHS = \frac{2sin \theta cos \theta - cos \theta }{1-sin \theta + sin^{2}\theta - cos^{2} \theta}$

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

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/* By Trigonometric Identity */

• cos² A = 1- sin² A

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

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

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

$= \frac{cos \theta }{sin \theta } \\= cot \theta \\= RHS$

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