sin x (-sin3x)/Sin²x-Cos ²x =2sinx
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Let. y = sin^4(x)+cos^4(x)
y. = [sin^2(x)+cos^2(x)]^2–2.sin^2(x).cos^2(x)
y. = 1 -2.(sin x.cos x)^2
y. = 1 -2(1/2.sin 2x)^2
y. = 1 - 1/2. (sin 2x)^2
For greatest value of y , sin 2x should be smallest . smallest value of sin2x are -1
or 0 .
(1) If sin 2x= -1 , and (sin 2x)^2 = +1
Thus, the greatest value of y will decrease.
(2). If sin 2x=0 , and (sin 2x)^2 also zero.
Thus , greatest value of y = 1 - 1/2.(0). = 1. Answer.
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