Question

Daca tg x =2
atunci
[tex]cos (2x)=?
[/tex]

Answer 1

tg(x) = sin(x) / cos(x) <=>

tg^2(x) = sin^2(x) / cos^2(x) | adaugam 1

tg^2(x) + 1 = (sin^2(x) + cos^2(x)) / cos^2(x)

tg^2(x) + 1 = 1/ cos^2(x)

tg^2(x) + 1 = 1 / ( 1/2 + 1/2 cos(2x) ) | aducem la puterea -1

1 / (tg^2(x) + 1 ) = 1/2 + 1/2 cos(2x)

pt tg(x) = 2

1 / 5 = 1 / 2 + 1 / 2 cos(2x)

2 / 5 = 1 + cos(2x)

cos(2x) = -3/5