Question

Se da expresia
E (x)=( sin x+cos x)totul la patrat .Calculati E (15°)

Answer 1

[tex]E(x)=(\sin x+\cos x)^2= \sin^2 x+\cos ^2 x+2\cdot \sin x\cdot \cos x\Rightarrow \\ \Rightarrow E(x)=1+\sin 2x\\ E(15\textdegree)=1+\sin 30\textdegree =1+\dfrac{1}{2}=\dfrac{3}{2}\\ \text{Identitati folosite:}\\ \boxed{\sin^2x+\cos^2 x=1 }\\\boxed{ 2\sin x\cos x=\sin 2x}[/tex]