prove sin(x)=-1

Solution

prove

sin (x) = - 1

False

Solution steps

sin (x) = - 1

Show that the two sides are not equal

For

sin (x) = - 1

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

sec (b) + tan (b) = \frac{cos ( b )}{1 - sin ( x )}

2 sinh (ln (x)) + \frac{1 ^{2}}{2} - \frac{4}{3} = 2

2 cot^{2} (x) sin^{2} (x) = 1 + cos (2 x)

\frac{1}{tan ( x )} - tan (x) = 2 cot (2 x)

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