Question

Show that:
`(1)/(1-cosx) -(1)/(1+cosx) = (2)/(sin x. tanx)`

Answer 1

Explanation:

`(1)/(1 - \cos(x) ) - (1)/(1 + \cos(x) ) = (2)/( \sin(x) tan(x) )`

`\frac{1 + \cos(x) - (1 - \cos(x) }{1 - \cos {}^(2) (x) } = (2 )/( \sin(x) \tan(x) )`

`\frac{2 \cos(x) }{ \sin {}^(2) (x) } = (2)/( \sin(x) \tan(x) )`

`(2 \cos(x) )/( \sin(x) \sin(x) )`

`(2 \cot(x) )/( \sin(x) )`

`(2)/( \sin(x) \tan(x) )`