[Toán 9] C/m $\sin^6a + \cos^6a = 1 - 3\sin^2a.\cos^2a$

M

minhtuyb

a/
$$\Leftrightarrow (\sin^2+\cos^2)^3-3\sin^2\cos^2(\sin^2+\cos^2)=1-3\sin^2\cos^2\\ \Leftrightarrow 1^2-3\sin^2\cos^2.1=1-3\sin^2\cos^2\ \text{(True)}\\ \Rightarrow DPCM$$

b/
$$\Leftrightarrow (\sin^2-\cos^2)(\sin^2+\cos^2)=1-2\cos^2\\ \Leftrightarrow \sin^2-\cos^2=1-2\cos^2\\ \Leftrightarrow \sin^2+\cos^2=1\ \text{(True)}\\ \Rightarrow DPCM$$

c/
$$\Leftrightarrow \dfrac{\sin^2}{\cos^2}-\sin^2= \dfrac{\sin^2}{\cos^2}.sin^2\\ \Leftrightarrow \dfrac{1}{\cos^2}-1= \dfrac{\sin^2}{\cos^2}\\ \Leftrightarrow 1-\cos^2=\sin^2 \\ \Leftrightarrow \sin^2+\cos^2=1\ \text{(True)}\\ \Rightarrow DPCM$$
 
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