What is the value of (1-cos(0))/(2sin^2(0)) ?

The value of (1-cos(0))/(2sin^2(0)) is Undefined

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(1-cos(0))/(2sin^2(0))

\frac{1 - cos ( 0 )}{2 sin ^{2} ( 0 )}

Undefined

Solution steps

\frac{1 - cos ( 0 )}{2 sin ^{2} ( 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

= \frac{1 - 1}{2 \cdot 0 ^{2}}

= Undefined

\frac{14}{cos ( 2 5 ^{\circ} )}

cos (- \frac{7 2}{10})

5 (cos (27 0^{\circ}) + i sin (27 0^{\circ}))

48 sin (4 5^{\circ})

70 cos (22 9^{\circ})

What is the value of (1-cos(0))/(2sin^2(0)) ?
The value of (1-cos(0))/(2sin^2(0)) is Undefined