Question

Rút gọn các biểu thức:

a)\(\sin^4\alpha+\cos^4\alpha+2\sin^2\alpha.\cos^2\alpha\)\

b) \(\sin^6\alpha+\cos^6\alpha+3\sin^2\alpha.\cos^2\alpha\)

Answer 1

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

Answer 2

b) \(sin^6a+cos^6a+3sin^2a.cos^2a=\left(sin^2a+cos^2a\right)\left(sin^4a-sin^2a.cos^2a+cos^4a\right)+3sin^2a.cos^2a=sin^4a+2sin^2a.cos^2a+cos^4a=\left(sin^2a+cos^2a\right)^2=1\)