Exams › SSC CGL (Prelims) › General

If \(\tan\theta=\frac{p-1}{p}\), find \(\sec^2\theta\).

1. \(\frac{p^2+1}{p^2+1}\)
2. \(\frac{p^2+1}{p^2-1}\)
3. \(\frac{p^2-1}{p^2+1}\)
4. \(\frac{p^2+1}{p^2+2}\)

Correct answer: \(\frac{p^2+1}{p^2-1}\)

Solution

Use \(\sec^2\theta=1+\tan^2\theta\). Substituting \(\tan\theta=\frac{p-1}{p}\) and simplifying gives the required expression.

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