What is equal to g(x) = cos(x)/ cos(x) sin2(x) + cos3(x) for x ∈ (0,π/2)?

Question

What is equal to g(x) = cos(x)/ cos(x) sin²(x) + cos³(x) for x ∈ (0,π/2)?

Answer 1

so first lets factor out a cos(x) from the denominator:

cosx/(cosx(sin²x+cos²x)), sin²x+cos²x=1 so we can plug that in:

cosx/cosx(1)=1/1=1