有关同角三角函数的问题sina+sin^2a=1时,求cos^2a+cos^6a的值答案是【（3倍根号下5）-5】/2,
问题描述：
有关同角三角函数的问题
sina+sin^2a=1时,求cos^2a+cos^6a的值
答案是【（3倍根号下5）-5】/2,
答
解出sina=(根号5-1)/2
cos^2a+cos^6a
=sina+sin^3a
=(sina+sin^2a)+sina(sina+sin^2a)-2sin^2a
=1+sina-2sin^2a
=1+3sina-2(sina+sin^2a)
=1+3sina-2
=3sina-1
=【（3倍根号下5）-5】/2
答
解析：设sina=tt+t^2=1t^2+t-1=0delta=1+4=5t1=-1+√5/2t2=-1-√5/2(舍)sina=√5-1/2cos^2A+cos^6A=sinA+sin^3A=sinA+sinA(1-sinA)=sinA+sinA-(sinA)^2=2sinA-sin^2A=2sinA-(1-sinA)=3sinA-1=3*√5-1/2-1=3√5-5/2...