Question

1/1-cosα - 1/1+cosα=2cotα• cosecα​

Answer 1

see explanation

Explanation:

Using the identities

1 - cos²x = sin²x

cotx =
`(cosx)/(sinx)` , cosecx =
`(1)/(sinx)`

Consider the left side

`(1)/(1-cos\alpha )` -
`(1)/(1+cos\alpha )`

=
`(1+cos\alpha - (1-cos\alpha ))/((1-cos\alpha )(1+cos\alpha ))`

=
`(1+cos\alpha -1+cos\alpha )/(1-cos^2\alpha )`

=
`(2cos\alpha )/(sin^2\alpha )`

=
`(2cos\alpha )/(sin\alpha )` ×
`(1)/(sin\alpha )`

= 2cotα . cosecα

= right side , thus verified