Question

determinați x€(0,pi/2) pentru care cosx sin(pi/2-x)-sinx cos(pi/2-x)=1/2​

Answer 1

Răspuns:

x=π/6

Explicație pas cu pas:

folosim formula

sinαcosβ-sinβcosα=sin(α-β)

cu α=π/2-x

si

β=x

avem

sin(π/2-x-x)=1/2

sin(π/2-2x) =1/2

cos(-2x)=1/2

cos(2x)=1/2

2x=2kπ±arccos1/2

2x=2kπ±π/3

x=kπ±π/6

in (0;π/2) convine doar x=π/6