If - X - sin - - 7-12 - sin - - -12 - sin - - 3-12- Y - cos - - 7-12 - cos - - -12 - cos - - 3-12- - prove that x-y - y-x - 2 tan 2- - -

x = sin( θ #160; + 7π12) + sin( #10;θ #160; π #160; 12) + sin( #10;θ #160; + 3π12 #10;) #10; #10; 2sin( 2θ #160; + π #160; # ...

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Definition of Functions

If [ X = si...

Question

If $\begin{matrix} X = sin (θ + \frac{7 π}{12}) + sin (θ - \frac{π}{12}) + sin (θ + \frac{3 π}{12}), Y = cos (θ - \frac{7 π}{12}) + cos (θ - \frac{π}{12}) + cos (θ + \frac{3 π}{12}) p r o v e t h a t \frac{x}{y} - \frac{y}{x} = 2 tan 2 θ . \end{matrix}$

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x = sin (t + \frac{7 π}{12}) + sin (t - \frac{π}{12}) + sin (t + \frac{3 π}{12}),

y = cos (t + \frac{7 π}{12}) + cos (t - \frac{π}{12}) + cos (t + \frac{3 π}{12})

\frac{d}{d t} (\frac{x}{y} - \frac{y}{x})

t = \frac{π}{8}

x = sin (t + \frac{7 π}{12}) + sin (t - \frac{π}{12}) + sin (t + \frac{3 π}{12}),

y = cos (t + \frac{7 π}{12}) + cos (t - \frac{π}{12}) + cos (t + \frac{3 π}{12})

\frac{d}{d t} (\frac{x}{y} - \frac{y}{x})

t = \frac{π}{8}

x = sin (t + \frac{7 π}{12}) +

sin (t - \frac{π}{12}) + sin (t + \frac{3 π}{12}),

y = cos (t + \frac{7 π}{12}) + cos (t - \frac{π}{12}) + cos (t + \frac{3 π}{12})

\frac{d}{d t} (\frac{x}{y} - \frac{y}{x})

t = \frac{π}{8}

x = sin (t + \frac{7 π}{12}) + sin (t - \frac{π}{12}) + sin (t + \frac{3 π}{12})

y = cos (t + \frac{7 π}{12}) + cos (t - \frac{π}{12}) + cos (t + \frac{3 π}{12}),

\frac{d}{d t} (\frac{x}{y} - \frac{y}{x})

t = \frac{π}{8}

16 cot θ = 12

\frac{sin θ - cos θ}{sin θ + cos θ} =

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