y=2cos^2x+5sinx-s=2(1-sin^2)+5sinx-4=-2(1-sin^2)+5sinx-2=-2(sinx-5/4)^2+9/8 这货是怎么配方的的?...

题目

y=2cos^2x+5sinx-s=2(1-sin^2)+5sinx-4=-2(1-sin^2)+5sinx-2=-2(sinx-5/4)^2+9/8 这货是怎么配方的的?...
y=2cos^2x+5sinx-s=2(1-sin^2)+5sinx-4=-2(1-sin^2)+5sinx-2=-2(sinx-5/4)^2+9/8 这货是怎么配方的的?不懂 还有这个f(x)=3cos^2x-4cosx-1=3(cosx-2/3)^2-7/3 谢您

答案

y=2(cosx)^2+5sinx-4
(cosx)^2+(sinx)^2=1
=2[1-(sinx)^2]+5sinx-4
=-2(sinx)^2+5sinx-2
=-2[(sinx)^2-5sinx/2]-2
(sinx-5/2)^2=(sinx)^2-5sinx+5^2/4
=-2[(sinx-5/2)^2-5^2/4]-2
=-2(sinx-5/2)^2+9/8