Răspuns:
Explicație pas cu pas:
[tex]Ex1. (sin^{2}\frac{\pi }{8}-cos^{2}\frac{\pi }{8})^{2}=(cos^{2}\frac{\pi }{8}-sin^{2}\frac{\pi }{8})^{2}=(cos(2*\frac{\pi }{8}))^{2}=(cos\frac{\pi }{4})^{2}=(\frac{\sqrt{2} }{2})^{2}=\frac{2}{4}=\frac{1}{2}[/tex]
Ex 2. sinα=1/2 ⇒cosα=√(3/4)= √3/ 2, reese di relatia sin²α+cos²α=1.
La fel sinβ=2/3 ⇒cosβ=√5/ 3. Atunci
sin2α=2sinα·cosα=2·(1/2)·(√3/ 2)=√3/ 2
cos2α=cos²α-sin²α=(√3/ 2)²-(1/2)²=(3/4)-(1/4)=2/4=1/2.
sin(α+β)=sinα·cosβ+cosα·sinβ=(1/2)·(√5/ 3)+(√3/ 2)·(2/3)=(√5/ 6)+(2√3)/6=(√5+2√3)/6.
cos(α-β)=cosα·cosβ+sinα·sinβ=(√3/ 2)·(√5/ 3)+(1/2)·(2/3)=√15/6+2/6
=(√15+2)/6
