We'll multiply by 2 cos x both
sides:
2 sin x * cos
x<1
Instead of the value 1, we'll put the
fundamental relation of trigonometry:
1= (sin x)^2 + (cos
x)^2
The inequality will
become:
2 sin x * cos x < (sin x)^2 + (cos
x)^2
We'll subtract 2sin x*cos x both
sides:
(sin x)^2 -2 sin x * cos x + (cos
x)^2>0
The expression from the left side is a
perfect square:
(sin x - cos x)^2 >
0, true, for any real value of x.
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