Question

Find the value of
2 cos(2*A)
when A
0
65​

Answer 1

✪ANSWER✪

The given expression has value 1.

᯽FORMULA᯽

$cos(A)cos(2A)cos(2²A).....cos(2ⁿ⁻¹ A) = \frac{sin(2ⁿA)}{2ⁿ sin(A)}$

★CALCULATION★

$[2cos(2⁰A)][2cos(2¹A)][2cos(2²A)][2cos(2³A)][2cos(2⁴A)][2cos(2⁵A)]$

$= 2⁶cos(2⁰A)cos(2¹A)cos(2²A)cos(2³A)cos(2⁴A)cos(2⁶⁻¹A)$

$=2⁶\times \frac{sin(2⁶A)}{2⁶sin(A)}$

$=\frac{sin(64A)}{sin(A)}$

$=\frac{sin(\frac{64π}{65})}{sin(\frac{π}{65})}$

$=\frac{sin(π -\frac{π}{65})}{sin(\frac{π}{65})}$

$=\frac{sin(\frac{π}{65})}{sin(\frac{π}{65})}$

$=1$