First slide

Multiple and sub- multiple Angles

Question

If $\sin^{2} A = x,$ then $\sin A s i n 2 A s i n 3 A s i n 4 A$ is a polynomial in x, the sum of whose coefficient is

Moderate

A

0
B

40
C

168
D

336

Solution

Let G.E be
$f (\sin A) = 2 \sin A (3 \sin A - 4 \sin^{3} A)$
$(1 - 2 \sin^{2} A) 4 \sin^{2} A (1 - \sin^{2} A)$
Put $\sin A = 1,$ sum of the coefficients = $f (1) = 0$

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