Question

[Ngô Chí Thành]

Rút gọn biểu thức \(\sqrt{sin^4x+4cos^2x}+\sqrt{cos^4x+4sin^2x}\) .

Answer 1

[Nguyễn Việt Lâm]

\(=\sqrt{sin^4x+4\left(1-sin^2x\right)}+\sqrt{cos^4x+4\left(1-cos^2x\right)}\)

\(=\sqrt{4-4sin^2x+sin^4x}+\sqrt{4-4cos^2x+cos^4x}\)

\(=\sqrt{\left(2-sin^2x\right)^2}+\sqrt{\left(2-cos^2x\right)^2}\)

\(=2-sin^2x+2-cos^2x=4-\left(sin^2x+cos^2x\right)\)

\(=3\)