<s>[INST] Find the value of $\sin \dfrac {\pi}{10} - \sin \dfrac {3\pi}{10}$ Find the value of $\sin \dfrac {\pi}{10} - \sin \dfrac {3\pi}{10}$
My Attempt:
$$\sin \dfrac {\pi}{10} - \sin \dfrac {3\pi}{10}$$
$$\sin \dfrac {180}{10} - \sin \dfrac {3\times 180}{10}$$
$$\sin 18^\circ - \sin 54^\circ$$
Now,
Let $A=18^\circ$.
$$5A=90^\circ$$
$$2A+3A=90^\circ$$
$$3A=90^\circ - 2A$$
Taking 'sin' on the both sides,
$$\sin 3A=\sin (90^\circ - 2A)$$
$$3\sin A-4\sin^3 A=\cos 2A$$
What should I do further?
 [/INST] $\cos 2A=1-2\sin^2 A$, then substitute $x=\sin A$.
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