Diketahui sin alfa - cos alfa = 2p. nilai sin 2 alfa =

Diketahui sin alfa – cos alfa = 2p.
nilai sin 2 alfa =

(sin α – cos α)² = (2p)²
sin²α -2 sinαcosα +cos²α = 4p²
sin²α + coss²α – 4p² = 2 sinαcosα
1 – 4p² = sin2α
jadi sin2α = 1 – 4p²

$sin alpha -cos alpha =2p\ (sin alpha -cos alpha)^2 =(2p)^2\ sin^2 alpha +cos^2 alpha -2.sin alpha .cos alpha =4p^2\ (1) - (sin 2 alpha )=4p^2\ sin 2 alpha =1-4p^2$