I'm struggling some with the us of trigonomic properties.

Question

The problem is integral sin(2x)sec(x) dx and I don't understand how sin(2x)sec(x) simplifies into 2sin(x).

Answer 1

sin(2x)sec(x)
= 2sinx cosx/cosx , basic identity look in your notes
= 2sinx

so ∫sin(2x)secx dx
= ∫ 2sinx dx
= -2cosx + c