Question

Bài 1: Cho a là góc nhọn . Rút gọn biểu thức

A= sin⁶a + cos⁶a+ 3sin²a-cos² a

Answer 1

ta có : \(A=sin^6a+cos^6a+3sin^2a-cos^2a\)

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

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

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

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

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

\(=\left(3sin^2a+1\right)\left(sin^2a\right)=3sin^4a+sin^2a\)