Question

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

sin (x) tan (x) sec (x) = ?

Answer 1

the answer is cot 2(x)

Answer 2

(tan^2(x))

Explanation:

We know that:

`tan (x) = (sin(x))/(cos(x))`

and

`sec(x)=(1)/(cos(x))`

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

`sin (x) * tan (x) * sec (x)`

`sin(x) * (sin(x))/(cos(x))*(1)/(cos(x))`

`(sin(x))/(1) *(sin(x))/(cos(x)) * (1)/(cos(x))`

Now multiplying the fractions together to get:

`((sin(x) * sin(x) * 1))/((cos(x) * cos(x)) )`

`((sin^2(x)))/((cos^2(x)) )`

Now since
`tan (x) = ((sin(x)))/((cos(x)))` so it follows that
`tan^2(x) = ((sin^2(x)))/((cos^2(x)))`

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