Question

if `cos theta +sin theta=1`,then prove that `cos theta-sin theta=(+) or (-) 1`?

Answer 1

Using the formula

`(a+b)^2+(a-b)^2=2(a^2+b^2)`

`(costheta+sintheta)^2+(costheta-sintheta)^2=2(sin^2theta+cos^2theta)`

`=>1^2+(costheta-sintheta)^2=2xx1`

`=>(costheta-sintheta)^2=2-1=1`

`=>costheta-sintheta=pm1`