Răspuns:
Explicație pas cu pas:
folosim urmatoarele formule:
sin(x - y) = sin(x)*cos(y) - cos(x)*sin(y)
sin(-x) = - sin(x) ⇒ sin²(-x) = [sin(-x)]² = [-sin(x)]² = sin²(x)
si valorile cunoscute: sin(3π/2) = -1 ; cos(3π/2)=0
Asadar:
sin²(π/2 - x) = sin²(x - π/2) = [sin(x - π/2)]² = [sin(x - π/2 + π - π)]² =
= [sin(x + π - 3π/2)]² = {sin[(x + π) - 3π/2]}² =
= [sin(x + π)*cos(3π/2) - cos(x + π)*sin(3π/2)]² = [sin(x + π)*0 - cos(x + π)*(-1)]² =
= [cos(x + π)]² = cos²(x + π)
Si atunci
sin²(π/2 - x) + sin²(x + π) = cos²(x + π) + sin²(x + π) = 1
