Question

Cho a là góc nhọn. Rút gọn biểu thức:     A=sin⁶a + cos⁶a + 3sin²a . cos²a

Answer 1

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

=\(\left(sin^2a+cos^2a\right)\left(sin^4a-cos^2asin^2a+cos^4a\right)+3sin^2acos^2a\)

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

Answer 2

( tan²a+cot a)^{2 _}  ( tan a - cot a )²