Question

（1)已知cosa=4/5,求（sina）^4+（cosa）^4

Answer 1

(1)因为cosa=4/5,所以（cosa）^2=16/25,（sina）^2=9/25

(sina)^4+(cosa)^4

=[(sina)^2+(cosa)^2]^2-2(sina)^2(cosa)^2

=1-2 * 9/25 * 16/25

=337/625

(2)因为sina+cosa=1/2,所以(sina+cosa)^2=1/4

(sina)^2+(cosa)^2+2*sina*cosa=1+sin2a=1/4

所以sin2a=-3/4

(3)[sin(a/2)]^2+[cos(a/2)]^2=1,2sin(a/2)cos(a/2)=sina

[根号（1-sina)]+[根号（1+sina）]

=根号{[sin(a/2)]^2+[cos(a/2)]^2-2sin(a/2)cos(a/2)}+根号{[sin(a/2)]^2+[cos(a/2)]^2+2sin(a/2)cos(a/2)]}

=根号{[sin(a/2)-cos(a/2)]^2}+根号{[sin(a/2)+cos(a/2)]^2}

因为a属于（1.5派,2派）,所以a/2属于（3/4派,派）,

所以sin(a/2)-cos(a/2)>0,sin(a/2)+cos(a/2)