Lượng giác lớp 10

K

kute2linh

$A$= $\sqrt[]{sin^4x+ 4cos^2x} + \sqrt[]{cos^4x+4sin^2x}$

= $\sqrt[]{(sin^2x)^2 + 4cos^2x}+ \sqrt[]{(cos^2x)^2+ 4sin^2x}$

= $\sqrt[]{(1-cos^2x)^2 + 4cos^2x}+ \sqrt[]{(1-sin^2x)^2+ 4sin^2x}$

= $ \sqrt[]{1-2cos^2x+ cos^4x+ 4cos^2x} + \sqrt[]{1- 2sin^2x+ sin^4x+ 4sin^2x }$

= $ 1+ cos ^2x +1+ sin^2x$

=$3$
 
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