If n = 1,2,3, ..., then 4 ... 2^ n-1 is equal to: 1. 2 n 2n 2. 2^… - Vidyadip

Question

If n = 1,2,3, ..., then $\cos\alpha\cos4\alpha\ ...\cos2^{\text{n}-1}\alpha$ is equal to:

$\frac{\sin2\text{n}\alpha}{2\text{n}\sin\alpha}$
$\frac{\sin2^\text{n}\alpha}{2^\text{n}\sin2^{\text{n}-1}\alpha}$
$\frac{\sin4^{\text{n}-1}\alpha}{4^{\text{n}-1}\sin\alpha}$
$\frac{\sin4^{\text{n}-1}\alpha}{4^{\text{n}-1}\sin\alpha}$

✓

Answer

$\frac{\sin4^{\text{n}-1}\alpha}{4^{\text{n}-1}\sin\alpha}$

Solution:

$\therefore\cos\alpha\cos2\alpha\cos4\alpha\ ...\cos2^{\text{n}-1}\alpha=\frac{\sin2^\text{n}\alpha}{2^\text{n}\sin\alpha}$

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