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Byju's Answer

Standard XII

Mathematics

Principal Solution of Trigonometric Equation

If tanh x=1...

Question

If $tanh x = 1 / 2$ , then the value of $tanh (3 x) =$

14 / 13

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14 / 15

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15 / 13

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13 / 14

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Solution

The correct option is D $13 / 14$
Given $tanh x = \frac{1}{2}$

$tanh (3 x) = \frac{3 tanh x + {tanh}^{3} x}{1 + 3 {tanh}^{2} x} = \frac{\frac{3}{2} + \frac{1}{8}}{1 + \frac{3}{4}} = \frac{\frac{12 + 1}{8}}{\frac{4 + 3}{4}} = \frac{13}{14}$

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If tanhx=1/2, then the value of tanh (3x)=

The correct option is D 13/14Given tanhx=12tanh(3x)=3tanhx+tanh3x1+3tanh2x=32+181+34=12+184+34=1314

If $tanh x = 1 / 2$ , then the value of $tanh (3 x) =$

The correct option is D $13 / 14$
Given $tanh x = \frac{1}{2}$

$tanh (3 x) = \frac{3 tanh x + {tanh}^{3} x}{1 + 3 {tanh}^{2} x} = \frac{\frac{3}{2} + \frac{1}{8}}{1 + \frac{3}{4}} = \frac{\frac{12 + 1}{8}}{\frac{4 + 3}{4}} = \frac{13}{14}$