Mar 3, 2014 Thread starter Admin #1 anemone MHB POTW Director Staff member Feb 14, 2012 3,967 Show that the trigonometric equation $\sin (\cos a)= \cos (\sin a)$ has no solutions.
Mar 3, 2014 #2 kaliprasad Well-known member Mar 31, 2013 1,358 anemone said: Show that the trigonometric equation $\sin (\cos a)= \cos (\sin a)$ has no solutions. Click to expand... Spoiler 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
anemone said: Show that the trigonometric equation $\sin (\cos a)= \cos (\sin a)$ has no solutions. Click to expand... Spoiler 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