AP EAMCET · Maths · Trigonometric Equations
If \((1+\tan \alpha)(1+\tan 4 \alpha)=2, \alpha \in\left(0, \frac{\pi}{16}\right)\), then \(\alpha\) is equal to
- A \(\frac{\pi}{20}\)
- B \(\frac{\pi}{30}\)
- C \(\frac{\pi}{40}\)
- D \(\frac{\pi}{60}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{20}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given that }(1+\tan \alpha)(1+\tan 4 \alpha)=2, \alpha \in\left(0, \frac{\pi}{16}\right) \\ & \Rightarrow 1+\tan \alpha+\tan 4 \alpha+\tan \alpha \tan 4 \alpha=2 \\ & \Rightarrow \quad \tan \alpha+\tan 4 \alpha=1-\tan \alpha \tan 4 \alpha \\ &…
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