Question

Prove
1/(cosec A-cot A) - 1/ sinA=1/sin A - 1/(cosec A - cot A)

Answer 1

Hope the image helps.you

Answer 2

Step-by-step explanation:

$\frac{1}{cosec \: a - cot \: a} - \frac{1}{ \sin \: a } = \frac{1}{sin \: a} - \frac{1}{cosec \: a \: - cot \: a}$

$or \: \: \frac{1}{cosec \: a - cot \: a} + \frac{1}{cosec \: a \: + cot \: a \: } = \frac{1}{sin \: a } + \frac{1}{sin \: a} = \frac{2}{sin \: a \: }$

$lhs =$

$= > \frac{(cosec \: a \: + cot \: a) + (cosec \: a \: - cot \: a)}{cosec \: a - cot \: a} (cosec \: a \: + cot \: a)$

$= > \frac{2cosec \: a}{cosec {}^{2}a \: - cot {}^{2} a }$

$= > \frac{2cosec \: a \: }{1}$

$= > \frac{2}{sin \: a}$

$= > rhs$

$hence \: proved$