Question

[ngoclinhnguyen]

Cho α ∈ (0;\(\dfrac{\Pi}{2}\)) và tan α = 3. Khi đó sin(α +π) bằng

Answer 1

[Ngô Thành Chung]

do a ∈ \(\left(0;\dfrac{\pi}{2}\right)\)⇒ \(\left\{{}\begin{matrix}sinx>0\\cosx>0\end{matrix}\right.\)

Mà tanx = 3 ⇒ \(\dfrac{sinx}{cosx}=3\Leftrightarrow\dfrac{sin^2x}{cos^2x}=9\Rightarrow10sin^2x=9\)

⇒ sinx = \(\dfrac{3}{\sqrt{10}}\)

⇒ sin (x + π) = -sinx = -\(\dfrac{3}{\sqrt{10}}\)