$s i n 3 A = 3 s i n A - 4 s i n^{3} A$
If true then write 1 and if false then write 0

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Solution

Given, $A = 30^{\circ}$
Now, $sin 3 A = 3 sin A - 4 {sin}^{3} A$
L.H.S: $sin 3 A = sin 3 \times 30^{0} = sin 90^{\circ} = 1$
R.H.S. $3 sin A - 4 s i n^{3} A = 3 sin 30^{o} - 4 {sin}^{3} 30^{o}$
= $3 (\frac{1}{2}) - 4 (\frac{1}{2})^{3}$
= $\frac{3}{2} - 4 \frac{1}{8}$
= $\frac{3}{2} - \frac{1}{2}$
= $1$
Thus, $L . H . S = R . H . S$

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