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Show the trigonometric equation has no solutions

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Thread starter anemone
Start date Mar 3, 2014
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Trigonometric Trigonometric equation

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anemone

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Thread starter
Mar 3, 2014

#1

Show that the trigonometric equation $\sin (\cos a)= \cos (\sin a)$ has no solutions.

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kaliprasad

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Mar 3, 2014

#2

anemone said:

Show that the trigonometric equation $\sin (\cos a)= \cos (\sin a)$ has no solutions.

if sin (x) = cos (y) then

$x+y = \pi/2 +2npi$ or $(2n+1)pi-\pi/2$

so lowest | cos a + sin a | = $\pi/2$

so |cos a + sin a| =$ \pi/2$ should have a solution

but |cos a + sin a | <= $\sqrt(2)$

so no solution

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