Question

chứng minh rằng cos^4a - sin^4a+1=2cos^2a

Answer 1

\(\cos^4\alpha-\sin^4\alpha+1\\ =\left(\sin^2\alpha+\cos^2\alpha\right)\left(-\sin^2\alpha+\cos^2\alpha\right)+\left(\sin^2\alpha+\cos^2\alpha\right)\\ =-\sin^2\alpha+\cos^2\alpha+\sin^2\alpha+\cos^2\alpha=2\cos^2\alpha\)

Answer 2

\(cos^4a-sin^4a+1=\left(cos^2a-sin^2a\right)\left(cos^2a+sin^2a\right)+1\)

\(=cos^2a-sin^2a+1=cos^2a-sin^2a+sin^2a+cos^2a=2cos^2a\)

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