Exams › SSC CGL (Prelims) › General

Given that tan(theta) + cot(theta) = 5 and tan(theta) * cot(theta) = 1, evaluate tan^2(theta) + cosec^2(theta).

1. 23
2. 24
3. 25
4. 26

Correct answer: 24

Solution

Since cosec^2 = 1 + cot^2, the target equals tan^2 + cot^2 + 1. From (tan+cot)^2 = 25 = tan^2 + cot^2 + 2, we get tan^2 + cot^2 = 23, so the answer is 23 + 1 = 24.

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