Question

[Phạm Nhật Trúc]

Giúp mình giải câu 113, 114

Answer 1

[Nguyễn Việt Lâm]

112.

\(sin\left(\dfrac{\pi}{2}-x\right)+cot^2x=cosx+\dfrac{cos^2x}{sin^2x}=cosx+\dfrac{cos^2x}{1-cos^2x}\)

\(=a+\dfrac{a^2}{1-a^2}=\dfrac{-a^3+a^2+a}{1-a^2}\)

\(\Rightarrow\left\{{}\begin{matrix}m=-1\\n=1\end{matrix}\right.\) \(\Rightarrow m-n=-3\)

114.

\(cos\left(\dfrac{\pi}{2}-x\right)+tan^2x=sinx+\dfrac{sin^2x}{cos^2x}=sinx+\dfrac{sin^2x}{1-sin^2x}\)

\(=a+\dfrac{a^2}{1-a^2}=\dfrac{-a^3+a^2+a}{1-a^2}\)

\(\Rightarrow\left\{{}\begin{matrix}m=-1\\n=1\end{matrix}\right.\) \(\Rightarrow5m+n=-4\)