Question: Simplify: (1+sinx-cos2x)/(cosx+sin2x).
Using the identities cos2x = 1 - 2.sin^2(x) and sin(2x) = 2.sin(x).cos(x), the expression simplifies to,
(1 + sin(x) - 1 + 2.sin^2(x))/(cos(x) + 2.sin(x).cos(x))
(sin(x) + 2.sin^2(x))/(cos(x) + 2.sin(x).cos(x))
[sin(x)(1 + 2.sin(x))]/[cos(x)(1 + 2.sin(x))]
sin(x)/cos(x)
tan(x)