已知cos(π/4-α)cos(π/4+α)=1/8,则sin^4α+cos^4α

问题描述:

已知cos(π/4-α)cos(π/4+α)=1/8,则sin^4α+cos^4α

cos(π/4-α)cos(π/4+α)=1/8[cos(π/4)cosα+sin(π/4)sinα][cos(π/4)cosα-sin(π/4)sinα]=1/8(1/2)(cosα+sinα)(cosα-sinα)=1/8(cosα+sinα)(cosα-sinα)=1/4cos²α-sin²α=1/4…………………...