Question

Prove csc-sin = cot^2/csc​

Answer 1

see explanation

Explanation:

Using the trigonometric identities

• cscx =
`(1)/(sinx)`

• cot²x =
`(cos^2x)/(sin^2x)`, sin²x + cos²x = 1

Consider the left side

cscx - sinx

=
`(1)/(sinx)` - sinx

=
`(1-sin^2x)/(sinx)`

=
`(cos^2x)/(sinx)` ×
`(sinx)/(sinx)`

=
`(cos^2x)/(sin^2x)` × sinx

= cot²x ×
`(1)/(cscx)`

=
`(cot^2x)/(cscx)` = right side ⇒ verified