Q64 / 160 · AP EAMCET 2009 · Mathematics
$\cos A \cos 2 A \cos 4 A \ldots \cos 2^{n-1} A$ equals
- Correct answerA$\frac{\sin 2^n A}{2^n \sin A}$
- B$\frac{2^n \sin 2^n A}{\sin A}$
- C$\frac{2^n \sin A}{\sin 2^n A}$
- D$\frac{\sin A}{2^n \sin 2^n A}$
Solution
It is a standard result.
$\begin{gathered}
\cos A \cos 2 A \cos 2^2 A \ldots \cos 2^{n-1} A \\
=\frac{\sin 2^n A}{2^n \sin A}
\end{gathered}$
Hence, the correct answer is option: 'A'.