A(0) = (cos 0 + sin 0)² + (cos 0 - sin 0)² → (1+0)² + (1-0)² = 2
A(π/4)=(cos π/4 + sin π/4)² + (cos π/4 - sin π/4)² → (√2/2+√2/2)² +(√2/2-√2)²= 2
A(π/4)=(cos π/3 + sin π/3)² + (cos π/3 - sin π/3)² → (1/2+√3/2)² +(1/2-√3/2)²= 2
∀x , A(x) = (cos x + sin x)² + (cos x - sin x)² →
A(x) = cos²x + 2sinxcosx + sin²x + cos²x - 2sinxcosx + sin²x = 2sin²x+2cos²x
A(x) = 2(sin²x+cos²x) = 2(1) = 2
Donc ∀x , (cos x + sin x)² + (cos x - sin x)² = 2
