If `sin(sinx+cosx)=cos(cosx-sinx),` and largest possible value of `sinxi spi/k ,` then the value of `k` is______.

Explanation

`sin(sinx+cosx)=cosx(cosx-sinx)`

`sin(sinx+cosx)=sin(pi/2-(cosx-sinx))`

`sinx+cosx=4pi+(-1)^n[pi/2-cosx+sinx]`

`sinx+cosx=pi/2-cosx+sinx`

`2cosx=pi/2`

`cosx=pi/4`

`cos^2x+sin^2x=1`

`sin^2x=1-pi^2/16`

...