Write the trigonometric expression in terms of sine and cosine, and then simplify. cos u + tan u sin u

Question

I really need help please and thanks 

Answer 1

We know that tan(u) = sin(u) / cos(u).

 

 

cos(u) + tan(u) sin(u) =

 

cos(u) + (sin(u) / cos(u)) sin(u) =

 

cos(u) + (sin²(u) / cos(u)) =

 

(cos²(u) + sin²(u)) / cos(u)

 

 

Knowing the identity   sin²(u) + cos²(u) = 1

 

 

1 / cos(u)