Question

Suppose cos(x) = -1/3, where π/2 is greater than or equal to x is greater than or equal to π. What is the value of tan(2x)?

A) -3/4
B) -4/3
C) 3/4
D) 4/3

Answer 1

The value of tan(2x) is (4√2 - 8) / 3.

Step-by-step explanation:

To find the value of tan(2x), we can use the identity: tan(2x) = 2tan(x) / (1 - tan^2(x)).

Given that cos(x) = -1/3, we can use the Pythagorean identity: sin^2(x) + cos^2(x) = 1, to find the value of sin(x). Since the range of x is from π/2 to π, sin(x) is negative. Therefore, sin(x) = -√(1 - cos^2(x)) = -√(1 - (-1/3)^2) = -2√2 / 3.

Substituting the values of sin(x) and cos(x) into the identity for tan(2x), we get: tan(2x) = 2(-2√2 / 3) / (1 - (-2√2 / 3)^2) = 4√2 / 3 - 8 / 3 = (4√2 - 8) / 3.