Question

Use trigonometric expressions to build an equivalent trigonometric identity with the given expression:

Answer 1

The answer is cot 2(x)

Answer 2

Answer:

(tan^2(x))

Step-by-step explanation:

We know that:

$tan (x) = \frac{sin(x)}{cos(x)}$

and

$sec(x)=\frac{1}{cos(x)}$

We will write everything in terms of sine and cosine to get:

$sin (x) * tan (x) * sec (x)$

$sin(x) * \frac{sin(x)}{cos(x)}*\frac{1}{cos(x)}$

$\frac{sin(x)}{1} *\frac{sin(x)}{cos(x)} * \frac{1}{cos(x)}$

Now multiplying the fractions together to get:

$\frac{(sin(x) * sin(x) * 1)}{(cos(x) * cos(x)) }$

$\frac{(sin^2(x))}{(cos^2(x)) }$

Now since $tan (x) = \frac{(sin(x))}{(cos(x))}$ so it follows that $tan^2(x) = \frac{(sin^2(x))}{(cos^2(x))}$

So the final answer is $(tan^2(x))$.