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Use the following information to determine tan(2x).

cos(x)=2/3 and sin(x) is negative

Sagot :

LammettHashidn

We have

tan(2x) = sin(2x) / cos(2x)

tan(2x) = (2 sin(x) cos(x)) / (2 cos²(x) - 1)

Recall that

sin²(x) + cos²(x) = 1

and since sin(x) is negative, it follows that

sin(x) = - √(1 - (2/3)²) = -√5/3

Then

tan(2x) = (2 (-√5/3) (2/3)) / (2 (2/3)² - 1) = 4√5

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