What is the value of -e^{cos(pi)}-(-e^{cos(0)}) ?

The value of -e^{cos(pi)}-(-e^{cos(0)}) is -1/e+e

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-e^{cos(pi)}-(-e^{cos(0)})

- e^{c o s (π)} - (- e^{c o s (0)})

- \frac{1}{e} + e

Decimal Notation

2.35040 \dots

Solution steps

- e^{c o s (π)} - (- e^{c o s (0)})

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= - e^{- 1} - (- e^{1})

Simplify

- e^{- 1} - (- e^{1}) : - \frac{1}{e} + e

- e^{- 1} - (- e^{1})

Apply rule

a^{1} = a

e^{1} = e

= - e^{- 1} - (- e)

Apply rule

- (- a) = a

= - e^{- 1} + e

Apply exponent rule:

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

= - \frac{1}{e} + e

= - \frac{1}{e} + e

1 + tan^{2} (31 5^{\circ})

- cos (4 \frac{π}{2})

arctan (\frac{16}{32})

- 2 (3.27) - e^{- 0.54} sin (3.27)

2 \cdot cos (\frac{3 π}{2})

What is the value of -e^{cos(pi)}-(-e^{cos(0)}) ?
The value of -e^{cos(pi)}-(-e^{cos(0)}) is -1/e+e