Question

Prove that
cot$\theta$ -tan$\theta$=$\frac{2cos^2\theta-1}{sin\theta cos\theta}$

Answer 1

$solution...............$

$let \: theta \: denotes \: by \: the \: symbol \: \alpha .$


$\cot \alpha - \tan \alpha$

$\frac{ \ \cos \alpha }{ \sin \alpha } - \frac{ \sin\alpha }{ \cos\alpha }$

$\frac{ { \cos }^{2} \alpha - { \sin }^{2} \alpha }{ \sin\alpha \cos \alpha }$

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

$\frac{ { \cos }^{2} \alpha - 1 + { \cos }^{2} \alpha }{ \sin\alpha \cos \alpha }$

$\frac{2 { \cos }^{2} \alpha - 1}{ \sin \alpha \cos \alpha }$

$hence........proved..........$

↪ Hope this will help you ↩

☞ ⛧⛧ By, Ⓜr. Thakur ⛧⛧