Question

Fie α ∈ ( [$\frac{ \pi }{2} , \frac{3 \pi }{4}$ ) astfel incat cos2x = $- \frac{ \sqrt{3} }{2}$ . Calculat cos α.

Answer 1

α ∈ [ π/2    , 3π/4]  cadranul II
cos 2x =  - √3/2 
cos2x = 2cos²x - 1 
2cos²x  = 1 + cos2x = 1 - √3 /2  = ( 2 - √3) / 2   impartim cu 2 
cos²x  = ( 2 - √3) /4 
cosx = +/-  rad( 2 - √3) / √4 
cad.II 
cosx = - √(2-√3) / 2