sin [tex] \sin(\pi + x) \sin(\pi + x) [/tex] (pi + x) sin (pi-x)

Materi : Trigonometri



-2 sinα sinβ = cos(α+β) - cos(α-β)
sinα sinβ = 1/2( cos(α-β) - cos(α+β) )

cos2α = 1 - 2 sin²α
sin²α = 1/2 (1 - cos2α)

π + x + π - x = 2π
π + x - π + x = 2x

sin(π + x) sin(π - x)
= 1/2 ( cos(2x) - cos(2π) )
= 1/2 (cos2x -  1)
= -sin²x