What is the maximum value of 10cos^2x -6sinxcosx +2sin^2x

Question

What is the maximum value of 10cos^2x -6sinxcosx +2sin^2x

Answer 1

f(x)=2−4sin2(x)+4sin(x)f(x)=2−4sin2⁡(x)+4sin⁡(x). Let t=sin(x)t=sin⁡(x). Then 00. We have a new function:

g(t)=−4t2+4t+2