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If cos(theta) = -1/2 and pi < theta < 3*pi/2, then the value of 4*tan²(theta) - 3*cosec²(theta) is:

1. 8
2. 6
3. 4
4. 12

Correct answer: 8

Solution

With cos(theta) = -1/2, sin²(theta) = 3/4, giving tan²(theta) = 3 and cosec²(theta) = 4/3, so the expression equals 12 - 4 = 8.

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