Is sin((9pi)/4)=sin(1/4 pi+2pi) ?

The answer to whether sin((9pi)/4)=sin(1/4 pi+2pi) is True

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prove sin((9pi)/4)=sin(1/4 pi+2pi)

prove

sin (\frac{9 π}{4}) = sin (\frac{1}{4} π + 2 π)

True

Solution steps

sin (\frac{9 π}{4}) = sin (\frac{1}{4} π + 2 π)

Manipulating left side

sin (\frac{9 π}{4})

Simplify

sin (\frac{9 π}{4}) : \frac{2}{2}

= \frac{2}{2}

Manipulating right side

sin (\frac{1}{4} π + 2 π)

Rewrite using trig identities

= \frac{2}{2}

We showed that the two sides could take the same form

\Rightarrow True

\frac{cos ( 2 x )}{1 - sin ( 2 x )} = \frac{1 + tan ( x )}{1 - tan ( x )}

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

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

(tan (x) + cot (x)) (sin (x) cos (x)) = 1

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

Is sin((9pi)/4)=sin(1/4 pi+2pi) ?
The answer to whether sin((9pi)/4)=sin(1/4 pi+2pi) is True