Question

Nu inteleg cum să-l rezolv​

Answer 1

$E(x) = \sin^2x+3\sin x\cdot \cos x +\cos^2 x \\ \\ \Rightarrow E = \sin^2 x+\cos^2 x+\dfrac{3}{2}\cdot 2\sin x\cdot \cos x \\ \\ \Rightarrow E(x) = 1+\dfrac{3}{2}\cdot \sin(2x)\\ \\ \Rightarrow E(\frac{\pi}{4}) = 1+\dfrac{3}{2}\cdot \sin\Big(2\cdot \dfrac{\pi}{4}\Big) \\ \\ \Rightarrow E(\frac{\pi}{4}) = 1+\dfrac{3}{2}\cdot \sin\Big(\dfrac{\pi}{2}\Big) \\ \\ \Rightarrow E(\frac{\pi}{4}) = 1+\dfrac{3}{2}\cdot 1 \\ \\ \Rightarrow \boxed{E\Big(\frac{\pi}{4}\Big) =\dfrac{5}{2}}$