Inverse Circular Functions Ques 29
- The value of $\tan \cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{2}{3}$ is
(1983, 1M)
(a) $\frac{6}{17}$
(b) $\frac{17}{6}$
(c) $\frac{16}{7}$
(d) None of these
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Answer:
Correct Answer: 29.(b)
Solution:
Formula:
Identities of Addition and Substraction:
- $\tan [\cos ^{-1} (\frac{4}{5})+\tan ^{-1} (\frac{2}{3})]=[\tan \tan ^{-1} (\frac{3}{4})+\tan ^{-1} (\frac{2}{3})]$
$ \because [\cos ^{-1} (\frac{4}{5})=\tan ^{-1} (\frac{3}{4})] $
$ =\tan [\tan ^{-1} (\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4} \cdot \frac{2}{3}})]=\tan [\tan ^{-1} (\frac{17}{6})]=\frac{17}{6} $
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