Question

Is sin theta minus cos theta = root 2 Sin Theta then prove that sin theta + cos theta is equals to root sin theta?

If `sintheta-costheta=sqrt(2)sintheta`, then prove that, `sintheta+costheta=-sqrt(2)costheta`

Answer 1

`sintheta+costheta=-sqrt(2)costheta`

Explanation:

Here,
`sintheta-costheta=sqrt(2)sintheta`
`=>sintheta-sqrt(2)sintheta=costheta`
`=>sintheta(1-sqrt(2))=costheta`
`=>sintheta[(1-sqrt(2))((1+sqrt(2))/(1+sqrt(2)))]=costheta`
`=>sintheta[(1-2)/(1+sqrt(2)))=costheta`
`=>sintheta(-1)=(1+sqrt(2))costheta`
`=>-sintheta=costheta+sqrt(2)costheta`
`=>-sintheta-costheta=sqrt(2)costheta`
`=>sintheta+costheta=-sqrt(2)costheta`