Prove that sinx-siny -2 sinx-y-2cosx-y-2 and hence show that sinx-sin3x-cosx- cos3x-tan2x

(sin3x+sinx/cos3x+cosx) =(2sin((3x+x/2)cos((3x x/2)/(2cos(3x+x/2)cos((3x x/2)) =(sin2x/cos2x)=tan2x ...

Prove that ...

Question

Prove that $s i n x + s i n y = 2 s i n \frac{x + y}{2} c o s \frac{x - y}{2}$ and hence show that $\frac{s i n x + s i n 3 x}{c o s x + c o s 3 x} = t a n 2 x$

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