What is (cosh(x))/(1+sinh^2(x)) ?

The solution to (cosh(x))/(1+sinh^2(x)) is sech(x)

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simplify (cosh(x))/(1+sinh^2(x))

simplify

\frac{cosh ( x )}{1 + sinh ^{2} ( x )}

sech (x)

Solution steps

\frac{cosh ( x )}{1 + sinh ^{2} ( x )}

Simplify

1 + sinh^{2} (x) : cosh^{2} (x)

= \frac{cosh ( x )}{cosh ^{2} ( x )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

cosh^{2} (x) = cosh (x) cosh (x)

= \frac{cosh ( x )}{cosh ( x ) cosh ( x )}

Cancel the common factor:

cosh (x)

= \frac{1}{cosh ( x )}

Use the Hyperbolic identity:

\frac{1}{cosh ( x )} = sech (x)

= sech (x)

(3 x + 5) (15 x + 230)

(2 x + 5) (3 x - 7)

(1 \frac{5}{7} x^{2 n - \frac{2}{3}})^{6} \cdot (\frac{7}{12} x^{\frac{1}{3}})^{6}

\frac{m ^{2} - 16}{m ^{2} + 7 m + 12} + \frac{m + 4}{( m + 3 ) ^{2}}

What is (cosh(x))/(1+sinh^2(x)) ?
The solution to (cosh(x))/(1+sinh^2(x)) is sech(x)