Find the maximum and minimum of the function y = 7-4sinxcosx + 2 (cosx) ^ 2-2 (SiNx) ^ 2

Y = 7-4sinxcosx + 2 (cosx) ^ 2-2 (SiNx) ^ 2 = 7-2sin2x + 2cos2x = 7-2 radical 2Sin (2x - π / 4)
Maximum 7 + 2 radical 2
Minimum 7-2 radical 2

Find the maximum and minimum value of the fourth power of y = cosx - sinx4

y=(cosx)^4-(sinx)^4
=[(cosx)^2+(sinx)^2][(cosx)^2-(sinx)^2)]
=cos(2x)
When x = k π (K ∈ z), there is ymax = 1
When x = k π + π / 2 (K ∈ z), there is Ymin = - 1

Y = the fourth power of SiNx + the maximum of cosx?

y=(sin²x+cos²x)-2sin²xcos²x
=1²-1/2*(2sinxcosx)²
=1-2sin²2x
-1

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