Exams › SSC CGL (Prelims) › General

If theta is an acute angle and tan(theta) + cot(theta) = 2, find the value of tan^2(theta) + cot^2(theta) + 2*tan^5(theta)*cot^4(theta).

1. 3
2. 4
3. 1
4. 2

Correct answer: 4

Solution

Since tan(theta) + cot(theta) = 2 and both are positive for acute angles, by AM-GM the minimum is 2, achieved only when tan(theta) = cot(theta) = 1 (theta = 45 degrees). Substituting: 1^2 + 1^2 + 2*(1^5)*(1^4) = 1 + 1 + 2 = 4.

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