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\(sin^6a+cos^6a=\left(sin^2a\right)^3+\left(cos^2a\right)^3\)

\(=\left(sin^2a+cos^2a\right)^3-3sin^2a.cos^2a\left(sin^2a+cos^2a\right)\)

\(=1-3sin^2a.cos^2a\)

d, \(\dfrac{\left(sinx+cosx\right)^2-1}{2cotx-sin2x}=tan^2x\)

\(\Leftrightarrow\dfrac{sin^2x+cos^2x+2sinx.cosx-1}{2cotx-sin2x}=tan^2x\)

\(\Leftrightarrow2sinx.cosx=tan^2x\left(2cotx-sin2x\right)\)

\(\Leftrightarrow2sinx.cosx=\dfrac{sin^2x}{cos^2x}\left(2\dfrac{cosx}{sinx}-2sinx.cosx\right)\)

\(\Leftrightarrow sinx.cosx=\dfrac{sinx}{cosx}-\dfrac{sin^3x}{cosx}\)

\(\Leftrightarrow sinx.cos^2x=sinx-sin^3x\)

\(\Leftrightarrow sinx.cos^2x=sinx\left(1-sin^2x\right)\)

\(\Leftrightarrow sinx.cos^2x=sinx.cos^2x\)

\(\Rightarrowđpcm\)

a, \(\left(1-sin^2x\right).tan^2x+\left(1-cos^2x\right).cot^2x=1\)

\(\Leftrightarrow cos^2x.\dfrac{sin^2x}{cos^2x}+sin^2x.\dfrac{cos^2x}{sin^2x}=1\)

\(\Leftrightarrow sin^2x+cos^2x=1\)

\(\Rightarrowđpcm\)

b, \(1-sin^2x-sin^2x.cot^2x=0\)

\(\Leftrightarrow cos^2x-cos^2x=0\)

\(\Rightarrowđpcm\)

c, \(cos^4x+sin^2x.cos^2x+sin^2x=1\)

\(\Leftrightarrow\left(cos^2x+sin^2x\right).cos^2x+sin^2x=1\)

\(\Leftrightarrow cos^2x+sin^2x=1\)

\(\Rightarrowđpcm\)

Đề thiếu. Bạn xem lại đề.