If costheta + sintheta =root 2 costheta then prove that costheta - sintheta =root2 sin theta

If costheta + sintheta =root 2 costheta then prove that costheta - sin

1.	If costheta + sintheta =root 2 costheta then prove that costheta - sintheta =root2 sin theta
Answer» I\'m taking A instead of theta.... cosA+sinA=root2 cosA.......... =>sinA=root2cosA-cosA...... =>sinA=cosA(root2-1).......... =>cosA=sinA/root2-1............ =>cosA=sinA(root2+1)/2-1.....(rationalise the denominator)......... =>cosA=root2sinA+sinA....... =>cosA-sinA=root2 sinA....... proved..?