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Q.

If $\cosh x = \frac{5}{4}$ , then $\tanh 3 x =$

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a

$\frac{25}{26}$

b

$\frac{63}{65}$

c

$\frac{65}{67}$

d

$\frac{252}{265}$

answer is A.

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Detailed Solution

$\cosh x = \frac{5}{4}$

$\cos h 3 x = 4 \cos h^{3} x - 3 \cos h x$

$= 4 {(\frac{5}{4})}^{3} - 3 (\frac{5}{4})$

$= \frac{65}{16}$

$\sin h 3 x = \frac{63}{16}$

$\tan h 3 x = \frac{63}{65}$

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