JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If \(A> 0, B > 0\) and \(A + B = \frac{\pi }{6}\), then the minimum value of \(tan\,A + tan\,B\) is
- A \(\sqrt 3 - \sqrt 2 \)
- B \( 4 - 2\sqrt 3 \)
- C \(\frac{2}{{\sqrt 3 }}\)
- D \(2 - \sqrt 3 \)
Answer & Solution
Correct Answer
(B) \( 4 - 2\sqrt 3 \)
Step-by-step Solution
Detailed explanation
\(\tan \,(A + B)\, = \,\frac{{\tan \,A\, + \tan \,B}}{{1 - \tan \,A\,\tan \,B}}\) \( \Rightarrow \,\frac{1}{{\sqrt 3 }}\, = \,\frac{y}{{1 - \tan \,A\,\tan \,B}}\) where \(y\, = \tan \,A\, + \tan \,B\) \( \Rightarrow \tan \,A\,\tan \,B\, = \,1 - \sqrt 3 y\) Also…
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