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27 tháng 10 2022

\(A=sin^6a+cos^6a+3\cdot sin^2a\cdot cos^2a\)

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

=1

9 tháng 11 2018

a) \(sin^6x+cos^6x+3sin^2x.cos^2x\)

\(=\left(sin^2x+cos^2x\right)\left(sin^4x-sin^2x.cox^2x+cos^4x\right)+3sin^2x.cos^2x\)

\(=sin^4x-sin^2x.cox^2x+cos^4x+3sin^2x.cos^2x\)

\(=sin^4x+2sin^2x.cox^2x+cos^4x=\left(sin^2x+cos^2x\right)^2=1\text{​​}\text{​}\)

b) \(sin^4x-cos^4x-\left(sinx+cosx\right)\left(sinx-cosx\right)\)

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

\(=1\left(sin^2x-cos^2x\right)-\left(sin^2x-cos^2x\right)=0\)

c) \(cos^2x+tan^2x.cos^2x\)

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

26 tháng 10 2014

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

\(=\left(sin^2\alpha+cos^2\alpha\right)\left(sin^4\alpha-sin^2\alpha.cos^2\alpha+cos^4\alpha\right)+3sin^2\alpha-cos^2\alpha\)

\(=sin^4\alpha-sin^2\alpha.cos^2\alpha+cos^4\alpha+3sin^2\alpha-cos^2\alpha\)

\(=sin^4\alpha+cos^4\alpha-sin^2\alpha.cos^2\alpha+3sin^2\alpha-cos^2\alpha\)

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

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

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

\(=1-3sin^2\alpha.\left(1-sin^2\alpha\right)+3sin^2\alpha-\left(1-sin^2\alpha\right)\)

\(=1-3sin^2\alpha-sin^2\alpha+3sin^2\alpha-\left(1-sin^2\alpha\right)\)

\(1-3sin^2\alpha-sin^2\alpha+3sin^2\alpha-1+sin^2\alpha\)

\(=0\)

31 tháng 7 2017

=(sin a+cos a)(sin^2.a-sina.cosa+cos^2a)+(sina+cosa)sina.cosa-cos a

=(sin a+cos a)(1-sina.cosa+sina.cosa)-cosa

=sina+cosa-cosa

=sina