If cos xa=sin xb then |a cos 2x+b sin 2x|=
|a|
|a√ab|
a2|b|
b2|a|
cosxa=sinxb ⇒tanx=ba sin 2x=2tanx1+tan2x=2aba2+b2cos2x=1−tan2x1+tan2x ⇒cos2x=1−b2a21+b2a2 ⇒cos2x=a2−b2a2+b2acos2x+bsin2x=a(a2−b2)a2+b2+b(2ab)a2+b2=a3−ab2+2ab2a2+b2=a3+ab2a2+b2=(a2+b2)a2+b2=a