Question

(1+2*sin a*cos a):sin a+cos a=?

Answer 1

Yuck, trig. I'm doing college trig at this very moment.

the top half (1+(2sinθ)cosθ)=1+sin(2θ)
because 2sinθcosθ=sin(2θ) is an identity

$\frac{1+sin2θ}{(sinθ) (cosθ)}$

Using polynomial division your answer becomes:
(csc θ)(sec θ)+2