What is the value of sech^2(2) ?

The value of sech^2(2) is (4e^4)/((e^4+1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sech^2(2)

sech^{2} (2)

\frac{4 e ^{4}}{( e ^{4} + 1 ) ^{2}}

Decimal Notation

0.07065 \dots

Solution steps

sech^{2} (2)

Rewrite using trig identities:

sech (2) = \frac{2 e ^{2}}{e ^{4} + 1}

sech (2)

Use the Hyperbolic identity:

sech (x) = \frac{2}{e ^{x} + e ^{- x}}

= \frac{2}{e ^{2} + e ^{- 2}}

\frac{2}{e ^{2} + e ^{- 2}} = \frac{2 e ^{2}}{e ^{4} + 1}

\frac{2}{e ^{2} + e ^{- 2}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{2}{e ^{2} + \frac{1}{e ^{2}}}

Join

e^{2} + \frac{1}{e ^{2}} : \frac{e ^{4} + 1}{e ^{2}}

e^{2} + \frac{1}{e ^{2}}

Convert element to fraction:

e^{2} = \frac{e ^{2} e ^{2}}{e ^{2}}

= \frac{e ^{2} e ^{2}}{e ^{2}} + \frac{1}{e ^{2}}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{e ^{2} e ^{2} + 1}{e ^{2}}

e^{2} e^{2} + 1 = e^{4} + 1

e^{2} e^{2} + 1

e^{2} e^{2} = e^{4}

e^{2} e^{2}

Apply exponent rule:

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

e^{2} e^{2} = e^{2 + 2}

= e^{2 + 2}

Add the numbers:

2 + 2 = 4

= e^{4}

= e^{4} + 1

= \frac{e ^{4} + 1}{e ^{2}}

= \frac{2}{\frac{e ^{4} + 1}{e ^{2}}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{2 e ^{2}}{e ^{4} + 1}

= \frac{2 e ^{2}}{e ^{4} + 1}

= (\frac{2 e ^{2}}{e ^{4} + 1})^{2}

Simplify

(\frac{2 e ^{2}}{e ^{4} + 1})^{2} : \frac{4 e ^{4}}{( e ^{4} + 1 ) ^{2}}

(\frac{2 e ^{2}}{e ^{4} + 1})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 2 e ^{2} ) ^{2}}{( e ^{4} + 1 ) ^{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 e^{2})^{2} = 2^{2} (e^{2})^{2}

= \frac{2 ^{2} ( e ^{2} ) ^{2}}{( e ^{4} + 1 ) ^{2}}

(e^{2})^{2} : e^{4}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= e^{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= e^{4}

= \frac{2 ^{2} e ^{4}}{( e ^{4} + 1 ) ^{2}}

2^{2} = 4

= \frac{4 e ^{4}}{( e ^{4} + 1 ) ^{2}}

= \frac{4 e ^{4}}{( e ^{4} + 1 ) ^{2}}

tan^{2} (\frac{π}{2}) [1 - sin (\frac{π}{2})]

arctan (\frac{- 12.231}{8.9996})

csc (18. 5^{\circ})

180 - arcsin (\frac{2}{5})

arctan (\frac{4}{- 9})