Diketahui sinα=p,α=lancip maka nilai sin2α-cos2α=….

Sin a = p

Sin a = depan / miring
Sin a = p/1

Depan = p
Miring = 1
Samping = √1²-p² = √1-p²

Sin²a - cos²a
= (p/1)² - ((√1-p²)/1)²
= (p²/1²) - ((1-p²)/1²)
= p² - (1-p²)
= p² - 1 + p²
= 2p² - 1

sin α = p
cos α = √(1 - p^2)
sin 2α = 2.sin α.cos α
sin 2α = 2.p.√(1 - p^2)
cos 2α = (cos α)^2 - (sin α)^2
cos 2α = (√(1 - p^2))^2- p^2
cos 2α = (1 - p^2) - p^2
cos 2α = 1 - 2p^2
jadi kalau
sin2α - cos 2α
= 2.p.√(1 - p^2) - (1 - 2p^2)
= 2p√(1 - p^2) - (1 - 2p^2)
= 2p√(1 - p^2) - 1 + 2p^2