Thursday, March 7, 2013

Verify the inequality : sinx

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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