What is the value of e^{cos(pi)}cos(pi)-e^{cos(pi)}sin^2(pi) ?

The value of e^{cos(pi)}cos(pi)-e^{cos(pi)}sin^2(pi) is -1/e

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e^{cos(pi)}cos(pi)-e^{cos(pi)}sin^2(pi)

e^{c o s (π)} cos (π) - e^{c o s (π)} sin^{2} (π)

- \frac{1}{e}

Decimal Notation

- 0.36787 \dots

Solution steps

e^{c o s (π)} cos (π) - e^{c o s (π)} sin^{2} (π)

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:

sin (π) = 0

sin (π)

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= e^{- 1} (- 1) - e^{- 1} \cdot 0^{2}

Simplify

e^{- 1} (- 1) - e^{- 1} \cdot 0^{2} : - \frac{1}{e}

e^{- 1} (- 1) - e^{- 1} \cdot 0^{2}

Apply rule

0^{a} = 0

0^{2} = 0

= (- 1) e^{- 1} - 0 \cdot e^{- 1}

Remove parentheses:

(- a) = - a

= - e^{- 1} \cdot 1 - e^{- 1} \cdot 0

Add similar elements:

- 1 \cdot e^{- 1} - 0 \cdot e^{- 1} = - e^{- 1}

= - e^{- 1}

Apply exponent rule:

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

= - \frac{1}{e}

= - \frac{1}{e}

cos (6 0^{\circ} + 22 5^{\circ})

2 sin (1 3^{\circ}) cos (1 3^{\circ})

- cos (\frac{π}{4}) - sin (\frac{π}{4})

15 \cdot cos (3 7^{\circ})

cos^{2} (16 0^{\circ})

What is the value of e^{cos(pi)}cos(pi)-e^{cos(pi)}sin^2(pi) ?
The value of e^{cos(pi)}cos(pi)-e^{cos(pi)}sin^2(pi) is -1/e