Answer:
(tan^2(x))
Step-by-step explanation:
We know that:
[tex]tan (x) = \frac{sin(x)}{cos(x)}[/tex]
and
[tex]sec(x)=\frac{1}{cos(x)}[/tex]
We will write everything in terms of sine and cosine to get:
[tex]sin (x) * tan (x) * sec (x)[/tex]
[tex]sin(x) * \frac{sin(x)}{cos(x)}*\frac{1}{cos(x)}[/tex]
[tex]\frac{sin(x)}{1} *\frac{sin(x)}{cos(x)} * \frac{1}{cos(x)}[/tex]
Now multiplying the fractions together to get:
[tex]\frac{(sin(x) * sin(x) * 1)}{(cos(x) * cos(x)) }[/tex]
[tex]\frac{(sin^2(x))}{(cos^2(x)) }[/tex]
Now since [tex]tan (x) = \frac{(sin(x))}{(cos(x))}[/tex] so it follows that [tex]tan^2(x) = \frac{(sin^2(x))}{(cos^2(x))}[/tex]
So the final answer is [tex](tan^2(x))[/tex].
