Is tan(pi/3)sin(2/3 pi)=1+sin(pi/6) ?

The answer to whether tan(pi/3)sin(2/3 pi)=1+sin(pi/6) is True

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prove tan(pi/3)sin(2/3 pi)=1+sin(pi/6)

prove

tan (\frac{π}{3}) sin (\frac{2}{3} π) = 1 + sin (\frac{π}{6})

True

Solution steps

tan (\frac{π}{3}) sin (\frac{2}{3} π) = 1 + sin (\frac{π}{6})

Manipulating left side

tan (\frac{π}{3}) sin (\frac{2}{3} π)

Simplify

sin (\frac{2}{3} π) tan (\frac{π}{3}) : \frac{3}{2}

= \frac{3}{2}

Manipulating right side

1 + sin (\frac{π}{6})

Simplify

1 + sin (\frac{π}{6}) : \frac{3}{2}

= \frac{3}{2}

We showed that the two sides could take the same form

\Rightarrow True

csc (2 x) = \frac{2 3}{3}

tan (x) = sin (x) - cos (x)

tan (\frac{11}{12} π) = tan (- \frac{π}{12})

cot (B) sec (B) sin (B) = 1

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

Is tan(pi/3)sin(2/3 pi)=1+sin(pi/6) ?
The answer to whether tan(pi/3)sin(2/3 pi)=1+sin(pi/6) is True