Establish the identity MAth question?

sec²β - 1 = tan²β by the Pythagorean identity.

Hi,

(sec β -1)(sec β +1)= tan² β

sec² β -1 = tan² β

1/cos² β -1 = sin² β/cos ² β

Multiply by cos² β

1 - cos² β = sin² β

sin² β + cos² β = 1 <= This proves that the original problem above is equivalent to a Pythagorean Identity.

I hope that helps!! :-)

(secβ - 1)(secβ + 1) = (1/cosβ - 1)(1/cosβ + 1)

         = ((1 - cosβ)/cosβ)((1 + cosβ)/cosβ)

         = (1 - cos²β)/cos²β

         = sin²β/cos²β

         = tan²β

Pythagorean identity: sin²θ + cos²θ = 1