express cosθ-sinθ as a cosine angleplease give me total solutionand also plz tell me why we have to divide and multiply with root2

Multiply and divided √2 (because it's value where angle of both sine and cosine are same so that we can make a formula of cos x cosy- sinx Sony)

√2(1/√2 cosx- 1/√2 sinx)

= √2( cos(45°+X)

 

( because cos a cosb - sin a sin b = cos(a+b))

1/√2 =cos 45 = sin 45