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Popular >

cosh(i)

Solution

cosh (i)

Solution

cos (1)

+1

Solution steps

cosh (i)

Use the Hyperbolic identity:

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

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

Simplify

\frac{e ^{i} + e ^{- i}}{2} : \frac{cos ( 1 ) + i sin ( 1 ) + cos ( - 1 ) + i sin ( - 1 )}{2}

= \frac{cos ( 1 ) + i sin ( 1 ) + cos ( - 1 ) + i sin ( - 1 )}{2}

Use the following property:

sin (- x) = - sin (x)

sin (- 1) = - sin (1)

= \frac{cos ( 1 ) + i sin ( 1 ) + cos ( - 1 ) + i ( - sin ( 1 ) )}{2}

Use the following property:

cos (- x) = cos (x)

cos (- 1) = cos (1)

= \frac{cos ( 1 ) + i sin ( 1 ) + cos ( 1 ) + i ( - sin ( 1 ) )}{2}

Simplify

= cos (1)

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Frequently Asked Questions (FAQ)

What is the value of cosh(i) ?
The value of cosh(i) is cos(1)