Exams › SSC CGL (Prelims) › General

If \(\tan \theta + \cot \theta = 5\) and \(\tan \theta \cdot \cot \theta = 1\), find \(\tan^2 \theta + \csc^2 \theta\).

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

Correct answer: 24

Solution

From \(\tan\theta + \cot\theta = 5\) and \(\tan\theta\cot\theta = 1\), let \(x=\tan\theta\). Then \(x + 1/x = 5\), so \(x^2 - 5x + 1 = 0\). Using the valid value, we get \(\tan^2\theta + \csc^2\theta = 24\).

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