If cosh x = frac{4}{3},then 3 cosh x + 3^2 co | vedclass

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(A) Given $\cosh x = \frac{4}{3}$.We know the identity $\cosh 2x = 2 \cosh^2 x - 1$.$\cosh 2x = 2 \left(\frac{4}{3}\right)^2 - 1 = 2 \left(\frac{16}{9

Vedclass · Accepted Answer

$175$

Vedclass · Answer

(A) Given $\cosh x = \frac{4}{3}$.We know the identity $\cosh 2x = 2 \cosh^2 x - 1$.$\cosh 2x = 2 \left(\frac{4}{3}\right)^2 - 1 = 2 \left(\frac{16}{9}\right) - 1 = \frac{32}{9} - 1 = \frac{23}{9}$.We know the identity $\cosh 3x = 4 \cosh^3 x - 3 \cosh x$.$\cosh 3x = 4 \left(\frac{4}{3}\right)^3 - 3 \left(\frac{4}{3}\right) = 4 \left(\frac{64}{27}\right) - 4 = \frac{256}{27} - 4 = \frac{256 - 108}{27} = \frac{148}{27}$.Now,substitute these values into the expression $3 \cosh x + 9 \cosh 2x + 27 \cosh 3x$:$= 3 \left(\frac{4}{3}\right) + 9 \left(\frac{23}{9}\right) + 27 \left(\frac{148}{27}\right)$$= 4 + 23 + 148 = 175$.

If $\cosh x = \frac{4}{3}$,then $3 \cosh x + 3^2 \cosh 2x + 3^3 \cosh 3x = $

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