For all `theta` in `[0,pi/2]` show that the `"cos"(sintheta)geq"sin"(costheta)`

Explanation

We have,
`cos theta+sintheta=sqrt(2)[(1)/sqrt(2)cos theta+(1)/sqrt(2)sin theta]`
`=sqrt(2)sin(pi//4+theta)`
`theta cos theta+sin thetalesqrt(2)ltpi//2`
`therefore cos theta+sin thetaltpi//2`
or `cos thetaltpi//2-sin theta`
As `theta in (0,pi//2)` in which `sin theta` increases.
Taking `sin` on both the sides of Eq. i, we get
`sin(cos theta)ltsin(pi//2-sin theta)`
or `sin(cos theta)ltcos(sin theta)`
or `cos (sin theta)gtsin(cos theta)`