Question

Verify this identity starting from the left

Answer 1

see explanation

Explanation:

Using the trigonometric identities

• sin²x + cos²x = 1

• cot x =
`(cosx)/(sinx)`, csc x =
`(1)/(sinx)`

Consider the left side

`(1+cosx)/(1-cosx)` -
`(1-cosx)/(1+cosx)`

Expressing as a single fraction

=
`((1+cosx)^2-(1-cosx)^2)/((1-cosx)(1+cosx))`

Expand and simplify numerator/ denominator

=
`(1+2cosx+cos^2x-1+2cosx-cos^2x)/(1-cos^2x)`

=
`(4cosx)/(sin^2x)`

=
`(4cosx)/(sinx)` ×
`(1)/(sinx)`

= 4cotxcscx = right side ⇒ verified