prove sin(θ/2)=12-20

Solution

prove

sin (\frac{θ}{2}) = 12 - 20

False

Solution steps

sin (\frac{θ}{2}) = 12 - 20

Show that the two sides are not equal

For

sin (\frac{θ}{2}) = 12 - 20

plug in

θ = 0

sin (\frac{0}{2}) = 0

sin (\frac{0}{2})

Simplify

= sin (0)

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

= 0

The two sides are not equal

\Rightarrow False

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tan (\frac{4 π}{3} - \frac{π}{4}) = 2 - 3

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\frac{( 1 - sin ^{2} ( x ) )}{( 1 + cos ( x ) )} = cos (x)