Question

Cot theta - tan theta = 2 cos^2 theta - 1 / sin theta. Cos theta

Answer 1

$\huge\sf{\underline{\underline{Solution:}}}$


$\sf{R. H. S. = \frac{2Cos^{2}\theta - 1 }{Sin \: \theta . \: Cos \: \theta}}$

$\sf{ = \frac{2Cos^{2}\theta - ( {Sin}^{2} \theta + {Cos}^{2}\theta) }{Sin \: \theta \: . \: Cos \: \theta}}$

$\sf{ = \frac{2 {Cos}^{2}\theta - {Sin}^{2}\theta - {Cos}^{2} \theta }{Sin \: \theta \: . \: Cos \: \theta }}$

$\sf{ = \frac{ {Cos}^{2} \theta - {Sin}^{2} \theta}{Sin \: \theta \: . \: Cos \: \theta}}$

$\sf{ = \frac{ {Cos}^{2}\theta }{Sin \: \theta \: . \: Cos \: \theta} - \frac{ {Sin}^{2}\theta }{Sin \: \theta \: . \: Cos \: \theta}}$

$\sf{ = \frac{Cos \: \theta}{Sin \: \theta} - \frac{Sin \: \theta}{Cos \: \theta}}$

$\sf{= Cot \: \theta - Tan \: \theta}$

$\sf{= L. H. S.}$

$\huge\sf{\underline{\underline{Hence\: proved.}}}$

Answer 2

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