Is sin(pi/3)=cos(pi/6) ?

The answer to whether sin(pi/3)=cos(pi/6) is True

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prove sin(pi/3)=cos(pi/6)

prove

sin (\frac{π}{3}) = cos (\frac{π}{6})

True

Solution steps

sin (\frac{π}{3}) = cos (\frac{π}{6})

Manipulating left side

sin (\frac{π}{3})

Simplify

= \frac{3}{2}

Manipulating right side

cos (\frac{π}{6})

Simplify

= \frac{3}{2}

We showed that the two sides could take the same form

\Rightarrow True

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

cos (- \frac{π}{6}) = sin (\frac{2 π}{3})

sin (x + π) - sin (x) + 1 = 0

csc (x) = csc (x) cos^{2} (x) + sin (x)

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