What is the value of e^0+cos(pi/4+(3pi)/4) ?

The value of e^0+cos(pi/4+(3pi)/4) is 0

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e^0+cos(pi/4+(3pi)/4)

e^{0} + cos (\frac{π}{4} + \frac{3 π}{4})

0

Solution steps

e^{0} + cos (\frac{π}{4} + \frac{3 π}{4})

Simplify:

\frac{π}{4} + \frac{3 π}{4} = π

\frac{π}{4} + \frac{3 π}{4}

Apply rule

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

= \frac{π + 3 π}{4}

Add similar elements:

π + 3 π = 4 π

= \frac{4 π}{4}

Divide the numbers:

\frac{4}{4} = 1

= π

e^{0} + cos (π) = 1 + cos (π)

e^{0} + cos (π)

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 1 + cos (π)

= 1 + cos (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)

= 1 - 1

Simplify

= 0

tan (5 3^{\circ}) (30)

csc (6 5^{\circ})

2 arccot (e^{c s c (- 2)})

- 40 sin (0.588) - 60 cos (0.588)

\frac{tan ( 14 5 ^{\circ} ) - tan ( 8 5 ^{\circ} )}{1 + tan ( 14 5 ^{\circ} ) tan ( 8 5 ^{\circ} )}

What is the value of e^0+cos(pi/4+(3pi)/4) ?
The value of e^0+cos(pi/4+(3pi)/4) is 0