Question

已知sina-cosa/sina=cosa=1/3,cos^4(π/3+a)-cos^4(π/6-a)=要详细的解题

写错了是sina-cosa/sina-cosa=1/3,cos^4(π/3+a)-cos^4(π/6-a)=

Answer 1

（sina-cosa）/（sina+cosa）=1/3
∴3sina-3cosa=sina+cosa
∴sina=2cosa
∴tana=2
∴sin2a=2sinacoa
=2sinacosa/(sin²a+cos²a)
=(2sina/cosa)/(sin²a/cos²a+1)
=2tana/(tan²a+1)
=4/5
cos2a=(cos²a-sin²a)/(sin²a+cos²a)
=（1-tan²a)/(1+tan²a)
=-3/5
∴cos^4(π/3+a)-cos^4(π/6-a)
=cos^4[π/2-(π/6-a)]-cos^4(π/6-a)
=sin^4(π/6-a)-cos^4(π/6-a)
=[sin²(π/6-a)+cos²(π/6-a)][sin²(π/6-a)-cos²(π/6-a)]
=-[cos²(π/6-a)-sin²(π/6-a)]
=-cos(π/3-2a)
=sin2asinπ/3-cos2acosπ/3
=4/5*√3/2+3/5*1/2
=(4√3+3)/10

Answer 2

sina-cosa/sina=cosa=1/3

这部分是不是有问题，求正确的题目