[sinα+2cos(5π/2+α)]/[cos(π-α)-sin(π/2-α)]=-1/4
即(sinα-2sinα)/(-cosα-cosα)=-1/4,
所以sinα/(2cosα)=-1/4,
所以tanα=-1/2,
所以(sinα+cosα)平方
=1+2sinαcosα
=1+(2sinαcosα)/(sinα平方+cosα平方)
=1+(2tanα)/(tanα平方+1)
=1-4/5=1/5.