COMEDK · Maths · 8. Trigonometric Ratios & Identities
If \(\tan \theta+\tan 4 \theta+\tan 7 \theta=\tan \theta \tan 4 \theta \tan 7 \theta\) then the general solution is
- A \(\theta=\frac{n \pi}{4}\)
- B \(\theta=\frac{n \pi}{12}\)
- C \(\theta=\frac{n \pi}{6}\)
- D None of these
Answer & Solution
Correct Answer
(B) \(\theta=\frac{n \pi}{12}\)
Step-by-step Solution
Detailed explanation
We have, \(\tan \theta+\tan 4 \theta+\tan 7 \theta=\tan \theta \tan 4 \theta \tan 7 \theta\) \(\tan \theta+\tan 4 \theta=\tan \theta \tan 4 \theta \tan 7 \theta-\tan 7 \theta\) \(\tan \theta+\tan 4 \theta=-\tan 7 \theta(1-\tan \theta \tan 4 \theta)\)…
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