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Question: Answered & Verified by Expert
If \(\theta+\phi=\frac{\pi}{4}\), then \((1+\tan \theta)(1+\tan \phi)\) is equal to
MathematicsTrigonometric Ratios & IdentitiesWBJEEWBJEE 2011
Options:
  • A 1
  • B 2
  • C \(5 / 2\)
  • D \(1 / 3\)
Solution:
1238 Upvotes Verified Answer
The correct answer is: 2
\(\begin{aligned}
& \text { Hints: }(1+\tan \theta)\left(1+\frac{(1-\tan \theta)}{1+\tan \theta}\right) \\
& =(1+\tan \theta) \frac{2}{1+\tan \theta}=2
\end{aligned}\)

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