Answer:
h(x) = 3tan(x)
Explanation:
We can rewrite h(x) as an expression involving tanx by applying the trigonometric identities:
[tex]\boxed{\begin{minipage}{3cm}\displaystyle tan\theta=\frac{sin\theta}{cos\theta}\\\\\displaystyle sec\theta=\frac{1}{cos\theta} \\\\\displaystyle csc\theta =\frac{1}{sin\theta} \end{minipage}}[/tex]
[tex]\displaystyle h(x)=\frac{sec(x)}{csc(x)} +\frac{2sin(x)}{cos(x)}[/tex]
[tex]\displaystyle h(x)=(sec(x)\div csc(x))+\frac{2sin(x)}{cos(x)}[/tex]
[tex]\displaystyle h(x)=\left(\frac{1}{cos(x)} \div\frac{1}{sin(x)} \right)+\frac{2sin(x)}{cos(x)}[/tex]
[tex]\displaystyle h(x)=\left(\frac{1}{cos(x)} \times\frac{sin(x)}{1} \right)+\frac{2sin(x)}{cos(x)}[/tex]
[tex]\displaystyle h(x)=\frac{sin(x)}{cos(x)}+\frac{2sin(x)}{cos(x)}[/tex]
[tex]\displaystyle h(x)=\frac{3sin(x)}{cos(x)}[/tex]
[tex]\displaystyle h(x)=3\left(\frac{sin(x)}{cos(x)}\right)[/tex]
[tex]\bf h(x)=3tan(x)[/tex]