What is the value of e^0cos(0)-e^0sin(0) ?

The value of e^0cos(0)-e^0sin(0) is 1

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e^0cos(0)-e^0sin(0)

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

1

Solution steps

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

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

Use the following trivial identity:

sin (0) = 0

sin (0)

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

Simplify

= 1

\frac{sin ( 2 8 ^{\circ} )}{1 + cos ( 2 8 ^{\circ} )}

7 cos (\frac{3 π}{4})

60 cos (6 0^{\circ})

csc (\frac{- π}{4})

2 cos^{2} (\frac{3 π}{8}) - 1

What is the value of e^0cos(0)-e^0sin(0) ?
The value of e^0cos(0)-e^0sin(0) is 1