Question

Use the following information to determine tan(2x). tan(x) = -2÷square root of 2 and sin(x) is negative

Answer 1

tan(2x) = 2√2

Explanation:

You want tan(2x) when tan(x) is -2/√2 and x is a 4th-quadrant angle.

Double angle

The tangent double-angle identity is ...

tan(2x) = 2tan(x)/(1 -tan(x)²)

For tan(x) = -2/√2, this gives ...

tan(2x) = 2(-2/√2)/(1 -(-2/√2)²) = -2√2/(1 -2)

tan(2x) = 2√2

<95141404393>