Chứng minh rằng: ( sin³ x . sin³ x ) + ( cos³ x . cos³ x ) = 1 - 3sin² x . cos² x

2 câu trả lời

Ta xét

VT=(sin3x.sin3x)+(cos3x.cos3x)

=sin6x+cos6x

=(sin2x)3+(cos2x)3

=(sin2x+cos2x)(sin4x+cos4xsin2xcos2x)

=sin4x+cos4xsin2xcos2x

=(sin2x)2+(cos2x)2+2sin2xcos2x2sin2xcos2xsin2xcos2x

=(sin2x+cos2x)23sin2xcos2x

=13sin2xcos2x=VP.

VT=(sin3a.sin3a)+(cos3a.cos3a)

=cos6a+sin6a

=(cos2a)3+(sin2a)3

=(cos2a+sin2a)(cos4acos2a.sin2a+sin4a)

=cos4a+sin4asin2acos2a

=(cos2a+sin2a)22sin2acos2asin2acos2a

=13sin2acos2a

=VP

Câu hỏi trong lớp Xem thêm