- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,755

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

- Thread starter anemone
- Start date

- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,755

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

- Mar 31, 2013

- 1,322

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

$x+y = \pi/2 +2npi$ 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