Question

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

Answer 1

`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`
`sinx=sqrt(16-pi^2)/4`
`cosx+sinx=pi-(pi/2-cosx+sinx)`
`cosx+sinx=pi/2+cosx-sinx`
`2sinx=pi/2`
`sinx=pi/4`
`k=4`.