Question

Prove that Sec^2xcot^2x-cos^2xcsc^2x=1

Answer 1

see explanation

Explanation:

Using the trigonometric identities

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

• cot x =
`(cosx)/(sinx)`

Consider the left side

sec²x. cot²x - cos²x. csc²x

=
`(1)/(cos^2x)` ×
`(cos^2x)/(sin^2x)` - cos²x ×
`(1)/(sin^2x)`

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

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

=
`(sin^2x)/(sin^2x)` = 1 = right side ⇒ proven