Question

If \(y = \sec(\tan^{-1} x)\), then \(y\) at \(x = 1\) is equal to term is the sum of two preceding terms. Then, the common ratio of the G.P. is:

• A. \(\sqrt{2}\)
• B. \(\frac{\sqrt{2}}{2}\)
• C. 1
• D. \(\sqrt{2}\)

Answer 1

The Correct Option is A

Let \(\theta = \tan^{-1} x\) \(\Rightarrow \tan \theta = x\)
At \(x = 1\), \(\tan \theta = 1 \Rightarrow \theta = \frac{\pi}{4}\)
\[ \Rightarrow y = \sec \theta = \sec\left(\frac{\pi}{4}\right) = \sqrt{2} \]