Playing With Cosines

Geometry Level 2

1 2 x = cos ⁡ ( a ) cos ⁡ ( 2 a ) cos ⁡ ( 3 a ) ⋯ cos ⁡ ( 999 a ) \large \dfrac1{2^x} = \cos (a) \cos(2a) \cos(3a) \cdots \cos(999a)

The equation above holds true for a = 2 π 1999 a = \dfrac{2\pi}{1999} . Find x x .


The answer is 999.

View wiki
Dhanvanth Balakrishnan by Dhanvanth Balakrishnan , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

18 Helpful 0 Interesting 0 Brilliant 0 Confused

the step i which u cancel T is wwrong , check it once again!

A Former Brilliant Member - 4 years, 8 months ago

I also had posted this question earlier.

Aaron Jerry Ninan - 4 years, 8 months ago

It can also be solved if we consider the roots of z^1999=1

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Care to elaborate??

Aaghaz Mahajan - 2 years, 3 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...