Is sin(x)=(sqrt(2))/2 ?

The answer to whether sin(x)=(sqrt(2))/2 is False

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prove sin(x)=(sqrt(2))/2

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

sin (0) = 0

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

csc^{2} (x) (sec^{2} (x) - 1) = \frac{1}{cos ^{2} ( x )}

sin^{2} (0) = 4 (cos (- 0) - 1)

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

cos (\frac{π}{2} - x) sec (x) = tan (x)

cos (- x) + sin (- x) = cos (x) - sin (x)