Final answer:
If tan(x) < 6 and 180 < x < 270, the value of cos(x) is -√(36/37). Hence the correct answer is option A
Step-by-step explanation:
To find the value of cos(x), we can use the relationship between tan(x) and cos(x). Since tan(x) = opposite/adjacent = sin(x)/cos(x), we can write sin(x)/cos(x) < 6. To find cos(x), we need to solve the inequality. Since 180 < x < 270, this means x is in the third quadrant, where tan(x) is negative. Therefore, cos(x) will also be negative.
Now, let's find the absolute value of cos(x) by taking the reciprocal of the absolute value of tan(x). The absolute value of tan(x) is 6, so the absolute value of cos(x) is 1/6.
Since x is in the third quadrant, cos(x) will be negative. Therefore, the answer is Option (a) -√(36/37).