The value of reduced trigonometric ratio cos2a + Tan 2A. Cos2a

The value of reduced trigonometric ratio cos2a + Tan 2A. Cos2a

tan2a=sin2a/cos2a
So cos2a + tan2a. Cos2a = cos2a + (sin2a / cos2a) cos2a = cos2a + sin2a
=√2(sin2a*√2/2+cos2a*√2/2)
=√2(sin2acosπ/4+cos2asinπ/4)
=√2sin(2a+π/4)