prove sin(β)= 1/2

Solution

prove

sin (β) = \frac{1}{2}

False

Solution steps

sin (β) = \frac{1}{2}

Show that the two sides are not equal

For

sin (β) = \frac{1}{2}

plug in

β = 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

cos^{4} (θ) = \frac{1}{4} + \frac{cos ( 2 θ )}{2} + \frac{cos ^{2} ( 2 θ )}{4}

3 cos (t) - 3 cos (3 t) = 12 sin^{2} (t) cos (t)

sin (x) (tan^{2} (x) + 1) = tan (x) sec (x)

csc (u) = 2

\frac{csc ( x )}{cot ( x )} = csc (x) tan (x)