Question

Q27. The value of Cosh²x is equal to​

Answer 1

Given,

coshx = 5/2

We know that,

cosh(2x) = 2 cosh²x - 1

$\begin{gathered}cosh(2x) = 2( \frac{5}{2} ) ^{2} - 1 \\ \\ cosh(2x)= 2( \frac{25}{4} ) - 1 \\ \\ cosh(2x) = \frac{25}{2} - 1 \\ \\ cosh(2x) = \frac{25 - 2}{2} \\ \\ cosh(2x) = \frac{23}{2} \end{gathered}$

We also know that,

cosh²α - sinh²α = 1

$\begin{gathered}cosh ^{2} (2x) - sinh ^{2} (2x) = 1 \\ \\ cosh ^{2} (2x) - 1 = sinh ^{2} (2x) \\ \\ (\frac{23}{2} ) ^{2} - 1 = sinh^2(2x) \\ \\ sinh^2(2x) = \frac{529}{4} - 1 \\ \\ sinh ^{2} (2x) = \frac{525}{4} \\ \\ sinh(2x) = \sqrt{ \frac{525}{4} } \\ \\ sinh(2x) = \frac{5 \sqrt{21} }{2} \end{gathered}$

Therefore, sinh(2x) = 5√21/2, cosh(2x) = 23/2