C2. x∈[3;5]
(2sin7x*cos7x)² +(-cos14x)² =(sin5πx/2)/(sin5πx/2)+cos(4πx/3 -5π/6);
sin²14x +cos²14x = 1 +cos(4πx/3 -5π/6);
cos(4πx/3 -5π/6) =0 ;
4πx/3 -5π/6 =π/2 +πk ;
4πx/3 =4π/3 +πk ;
x=1 +3/4*k ;
3< 1 +3/4*k < 5 ;
2<3/4*k <4; <br>8/3 < k <16/3 ⇒ 3;4;5.<br>x₁+x₂ +x₃ =(1+3/4*3) +(1+3/4*4) +(1+3/4*5) =3 +(3+4+5)*3/4 =12 .
C3. y =3arctq( √2 +sinx - cosx)/2√2=3arctq( √2 +√2sin(x - π/4))/2√2=
3arctq( √2(1 +sin(x - π/4))/2√2 =3arctq(1 +sin(x - π/4))/2
sin(x - π/4)= -1 ⇒y =0 ;
sin(x - π/4) =1 ⇒y=3π/4
E(y) ∈ [ 0 ;3π/4].