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If Tan a = a A + 1 and Tan B = 1 2 a + 1 - Mathematics

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प्रश्न

If \[\tan A = \frac{a}{a + 1}\text{ and } \tan B = \frac{1}{2a + 1}\] 

विकल्प

  • (a) 0 

  • (b)\[\frac{\pi}{2}\] 

  • (c) \[\frac{\pi}{3}\] 

  • (d) \[\frac{\pi}{4}\] 

MCQ
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उत्तर

(d)\[\frac{\pi}{4}\] 

\[\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A\tan B} \]
\[ = \frac{\frac{a}{a + 1} + \frac{1}{2a + 1}}{1 - \frac{a}{\left( a + 1 \right)(2a + 1)}}\]
\[ = \frac{2 a^2 + a + a + 1}{2 a^2 + 3a + 1 - a}\]
\[ = \frac{2 a^2 + 2a + 1}{2 a^2 + 2a + 1}\]
\[ = 1\]
\[\text{ Therefore }, A + B = \tan^{- 1} (1) = \frac{\pi}{4} . \]

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अध्याय 7: Values of Trigonometric function at sum or difference of angles - Exercise 7.4 [पृष्ठ २७]

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आरडी शर्मा Mathematics [English] Class 11
अध्याय 7 Values of Trigonometric function at sum or difference of angles
Exercise 7.4 | Q 4 | पृष्ठ २७

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