Lời giải:
\(\sqrt{\sin ^4a+6\cos ^2a+3}+\sqrt{\cos ^4a+4\sin ^2a}=\sqrt{(1-\cos ^2a)^2+6\cos ^2a+3}+\sqrt{cos ^4a+4(1-\cos ^2a)}\)
\(=\sqrt{\cos ^4a+4\cos ^2a+4}+\sqrt{\cos ^4a-4\cos ^2a+4}\)
\(=\sqrt{(\cos ^2a+2)^2}+\sqrt{(\cos ^2a-2)^2}=|\cos ^2a+2|+|\cos ^2a-2|\)
\(=\cos ^2a+2+2-\cos ^2a=4\) (đpcm)
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\(=\sqrt{sin^4a+6-6sin^2a+3}+\sqrt{cos^4a+4-4cos^2a}\)
\(=\sqrt{\left(sin^2a-3\right)^2}+\sqrt{\left(cos^2a-2\right)^2}\)
\(=3-sin^2a+2-cos^2a\)
=5-1=4
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