Suppose cosine of x is equal to negative 1 third , where pi over 2 is less than or equal to x comma x is less than or equal to pi What is the value of tangent of 2 x ?

Since x is in quadrant II, sin x is positive. Using sin²x + cos²x = 1 gives sin x = √8/3, so tan x = (√8/3)/(-1/3) = -√8. Then tan 2x = 2 tan x/(1 − tan²x) = -2√8/(1 − 8) = 2√8/7, which is choice B.

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