Question

If sinh x = $\frac{3}{4}$, find cosh (2x) and sinh (2x).

Answer 1

Given that

sinh x =  3/4

Now

$cos h^{2}x=1+sin h^{2}x\\\\cos h^{2}x=1+(3/4)^{2}\\\\cos h^{2}x=1+9/16\\\\cos h^{2}x=25/16\\\\coshx=5/4$

Now

⇒ sinh (2x)

$sinh(2x)=2sinhx.coshx\\\\sinh(2x)=2(3/4).(5/4)\\\\sinh(2x)=15/8$

Also

⇒ cosh (2x)

$cosh2x=cosh^{2}x+sinh^{2}x\\\\cosh2x=(5/4)^{2}+(3/4)^{2}\\ \\cosh2x=\frac{25}{16}+\frac{9}{16}\\\\cosh2x=\frac{34}{16}$

Answer 2

Answer:

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