But I don't know all the values!

Geometry Level 1

$\cos(45^\circ) \times \cos(46^\circ) \times \cos(47^\circ) \times \ldots \times \cos(135^\circ ) = \ ?$

0

-1

1

\frac { \sqrt { 3 } }{ 2 }

6 solutions

Alan Enrique Ontiveros Salazar
Jun 11, 2015

In the product we find a term, which is $\cos(90^\circ)$ , and it is $0$ . Hence, all the product is $\boxed{0}$ .

Moderator note:

Yes, simple standard approach.

Bonus question : What would the answer be if all the cosine functions are replaced by tangent functions instead?

Answer to Bonus question 1 is not defined since tan90 is not defined.

Dinesh Nath Goswami - 6 years ago

for bonus: undefined, to be specific minus infinity

Alakh Aggarwal - 5 years, 11 months ago

How can it be $- \infty$ if it's undefined? If that was the case, surely it would be defined.

Michael Fuller - 5 years, 11 months ago

yeah true!! My mistake! :)

Alakh Aggarwal - 5 years, 11 months ago

It's undefined.

Animee World - 3 years, 3 months ago

Chris Brown
Apr 20, 2020

Eventually, everything will be multiplied by $\cos { \left( 90° \right) =0 }$ , and the rest will be multipled by $0$ , so the value of the whole series is $0$ .

Hadia Qadir
Aug 30, 2015

The answer is 0 because cos90 value is 0

Juan Valdiri
Jul 6, 2015

nice problem dude cos 90= 0 so pretty easy.

Hemanth Koundinya
Jun 17, 2015

since cos90 is 0 hence whole product is 0

Balaji Rajagopal
Jun 17, 2015

In that series cos 45 - cos 135 in between Cos90 is 0.

But I don't know all the values!

6 solutions

Moderator note:

0 pending reports