Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE A.) -2√8/7
B.) -√8
C.) √8
D.) 2√8/7

D

Step-by-step explanation:

We are given that:

And we want to find the value of tan(2x).

Note that since x is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

Using double angle identities:

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(x) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since x is in QII, cosine and tangent will be negative while sine will be positive. Hence:

Simplify:

Evaluate:

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

So, our answer is D.

28

step-by-step explanation:

8+8+6+6