If f is an even function then prove that $$\int _ { 0 } ^ { \pi / 2 } f ( \cos 2 x ) \cos x d x = \sqrt { 2 } \int _ { 0 } ^ { \pi / 4 } f ( \sin 2 x ) \cos x d x$$
The system of equations
If f is an even function then prove that $$\int _ { 0 } ^ { \pi / 2 } f ( \cos 2 x ) \cos x d x = \sqrt { 2 } \int _ { 0 } ^ { \pi / 4 } f ( \sin 2 x ) \cos x d x$$