Question

(1+sin4a-cos4a)/(1+sin4a+cos4a)=?

Answer 1

(1 + sin 4 a - cos 4 a) / (1 + sin 4 a + cos 4 a)

= (1 - cos 4 a + sin 4 a) / (1 + cos 4 a + sin 4 a)

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

= [2 (sin 2 a) (sin 2 a + cos 2 a)]/ [2 (cos 2 a) (cos 2 a + sin 2 a)]

= sin 2 a / cos 2 a

= tan 2 a .