4(tg^2a+sin^2a+cos^2a)cos^4a

= 4(sin^2a/cos^2a + sin^2a + cos^2a)cos^4a

= 4(sin^2a + sin^2a*cos^2a + cos^4a)cos^2a

= 4(sin^2a + sin^2a - sin^2acos^2a + cos^4a)cos^2a

= 4(2sin^2a - sin^2acos^2a + cos^4a)cos^2a

= 4(2sin^2a - sin^2a + cos^2a)cos^2a

= 4(2sin^2a - sin^2a + 1)cos^2a

= 8sin^2acos^2a - 4sin^4a + 4cos^2a