Question

Establish the identity.
sin theta * sec theta = tan theta

Answer 1

We are multiplying sin theta by sec theta, so we first start with valuing sec theta. Re-evaluate sec theta as sec(theta), and get the reciprocal.

`sin(theta) * (1)/(cos(theta))` <-- reciprocal

Combine sin() with the reciprocal of sec theta.

`(sin(theta))/(cos(theta))`

Rewrite this combination as tan(theta)

`tan(theta)`

Since the sides are equal, they count as an identity.

`sin(theta) * sec(theta) = tan(theta)`

That said, sin(theta) × sec(theta) = tan(theta) is an identity.

Answer 2

In the picture is how to solve it

Explanation: