Find the value of the given expression. tan(sin-1 35+cot-1 32) - Mathematics

प्रश्न

Find the value of the given expression.

$\tan (\sin^{- 1} \frac{3}{5} + \cot^{- 1} \frac{3}{2})$

योग

उत्तर

Let A = $\sin^{- 1} (\frac{3}{5}) and B = \cot^{- 1} (\frac{3}{2})$

$\sin A = \frac{3}{5} and \cot B = \frac{3}{2}$

$= \tan A = \frac{3}{4} and \tan B = \frac{2}{3}$

$\tan [\tan^{- 1} (\frac{3}{4}) + \tan^{- 1} (\frac{2}{3})] = [\tan^{- 1} (\frac{\frac{3}{4} + \frac{2}{3}}{1 - \frac{3}{4} \times \frac{2}{3}})]$

$= \tan [\tan^{- 1} (\frac{\frac{9 + 8}{12}}{1 - \frac{1}{2}})]$

$= \tan [\tan^{- 1} (\frac{17}{6})]$

$= \frac{17}{6}$

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Properties of Inverse Trigonometric Functions

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 18 Q 17 Q 19

अध्याय 2: Inverse Trigonometric Functions - Exercise 2.2 [पृष्ठ ४८]

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एनसीईआरटी Mathematics [English] Class 12

अध्याय 2 Inverse Trigonometric Functions
Exercise 2.2 | Q 18 | पृष्ठ ४८

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Find the value of the given expression. tan(sin-1 35+cot-1 32) - Mathematics

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