Question

已知sina=√5/5，则sin^4 (a)-cos^4 (a)的值为？

Answer 1

解：
sin⁴a-cos⁴a
=(sin²a+cos²a)(sin²a-cos²a)
=sin²a-1+sin²a
=2sin²a-1
=2(√5/5)²-1
=2/5-1
=-3/5

Answer 2

sin^4 (a)-cos^4 (a)
=(sin^2a+cos^2a)(sin^2a-cos^2a)
=-(cos^2a-sin^2a)
=-(1-2sin^2a)
=2sin^2-1
=2*(1/5)-1
=-3/5

Answer 3

sin^4 (a)-cos^4 (a)=(sin^2(a)-cos^2 (a))(sin^2 (a)+cos^2 (a))=(sin^2(a)-cos^2 (a))=cos2a
cos2a=1-2sin^2 (a)=1- 2*5/25=3/5

Answer 4

因为sina=√5/5，∴cosa=±√（1-5/25）=±2√5/5
∴原式=1/25-16/25
=-3/5

Answer 5

sin^4 (a)-cos^4 (a)
=（sin^2 (a)+cos^2 (a)）（sin^2 (a)-cos^2 (a)）
=1*（-cos2a)
=2sina*sina - 1
=2*1/5-1
=-3/5