Question

tìm a biết a là góc tù và sin⁴a + cos⁴a = 5/8

Answer 1

\(sin^4a+cos^4a=\dfrac{5}{8}\)

\(\Leftrightarrow\left(sin^2a+cos^2a\right)^2-2sin^2a.cos^2a=\dfrac{5}{8}\)

\(\Leftrightarrow1-2sin^2a\left(1-sin^2a\right)=\dfrac{5}{8}\)

\(\Leftrightarrow2sin^4a-2sin^2a+\dfrac{3}{8}=0\Rightarrow\left[{}\begin{matrix}sin^2a=\dfrac{3}{4}\\sin^2a=\dfrac{1}{4}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}sina=\dfrac{\sqrt{3}}{2}\\sina=\dfrac{1}{2}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}a=150^0\\a=120^0\end{matrix}\right.\)