Question

Prove or disprove the identity. if you find the identity is true, state the first line of the proof. if you find the identity is false, write the correct equation by replacing the right side. sec2 x(1 – sin2 x) = csc2 x cos x

Answer 1

False

Explanation:

Using the trigonometric identities

• sin²x + cos²x = 1

• secx =
`(1)/(cosx)`

Consider the left side

sec²x(1 - sin²x)

=
`(1)/(cos^2x)` × cos²x = 1

The correct identity is

sec²x(1 - sin²x) = 1