If cosx+sinx=sqrt (2) cosx then show that cosx-sinx=sqrt (2) sinx

Hello,

We suppose cos (x) ≠0 and sin (x) ≠0

cos (x) + sin (x) = √2 cos (x)

==>1+tg (x) = √2

==>tg (x) = √2-1

==>1/tg (x) = 1 / (√2-1)

==>cos (x) / sin (x) = √2+1

==>cos (x) = sin (x) + √2*sin (x)

==>cos (x) - sin (x) = √2 sin (x)