WBJEE · Maths · Trigonometric Ratios & Identities
Let \(f_n(x)=\tan \frac{x}{2}(1+\sec x)(1+\sec 2 x) \ldots\left(1+\sec 2^n x\right)\), then
- A \(f_5\left(\frac{\pi}{16}\right)=1\)
- B \(f_4\left(\frac{\pi}{16}\right)=1\)
- C \(f_3\left(\frac{\pi}{16}\right)=1\)
- D \(\mathrm{f}_2\left(\frac{\pi}{16}\right)=1\)
Answer & Solution
Correct Answer
(D) \(\mathrm{f}_2\left(\frac{\pi}{16}\right)=1\)
Step-by-step Solution
Detailed explanation
\(f_n(x)=\tan 2^n x, \quad f_5\left(\frac{\pi}{16}\right)=\tan \left(32 \cdot \frac{\pi}{16}\right)=0\)…
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