prove sin(pi/6)= 1/2

Solution

prove

sin (\frac{π}{6}) = \frac{1}{2}

True

Solution steps

sin (\frac{π}{6}) = \frac{1}{2}

Manipulating left side

sin (\frac{π}{6})

Simplify

= \frac{1}{2}

We showed that the two sides could take the same form

\Rightarrow True

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

(sin (t) - cos (t))^{2} = 1 - sin (2 t)

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

sin (θ) = \frac{2 tan ( \frac{θ}{2} )}{1 + tan ^{2} ( \frac{θ}{2} )}

sin^{2} (x) - 2 cos^{2} (x) = 1 - 3 cos^{2} (x)