Exams › SSC CGL (Prelims) › General

Find the value of tan^2(theta) + cot^2(theta) - sec^2(theta) * cosec^2(theta).

1. 2
2. -2
3. 0
4. 1/2

Correct answer: -2

Solution

tan^2+cot^2 = (sin^4+cos^4)/(sin^2 cos^2) = (1-2sin^2cos^2)/(sin^2cos^2). sec^2*cosec^2 = 1/(sin^2cos^2). Subtracting gives (1-2sin^2cos^2-1)/(sin^2cos^2) = -2sin^2cos^2/(sin^2cos^2) = -2.

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