Suppose cos(x)=-1/3, where pi/2≤x≤ pi. What is the value of tan(2x)?

4√2/7

Step-by-step explanation:

Suppose cos(x)=-1/3, where pi/2≤x≤ pi

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

Since sin2x = 2sinx cosx

cos 2x = 2cos²x-1

Substitute

tan(2x) = 2sinx cosx/ 2cos²x-1

Given cosx = -1/3

adjacent = -1

hyp = 3

opp = √3²-(-1)²

opp = √9-1

opp = √8

sinx = opp/hyp

sinx = √8/3

tan(2x) = 2sinx cosx/ 2cos²x-1

tan(2x) = 2(√8/3)(-1/3)/ 2(-1/3)²-1

tan2x= (-2√8/9 )÷ (2/9 - 1)

tan2x = -4√2/9 * 9/-7

tan 2x = 4√2/7

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation: