Easy - Peasy

Geometry Level 1

∏ i = 1 360 ( 3 − tan ⁡ 2 i ) 2 = ? \prod _{ i=1 }^{ 360 }{ \frac { (3-\tan ^{ 2 }{ i) } }{ 2 } } = ?

Note:- i i is in degrees. I know answer should be not defined but please don't multiply the not defined one.


The answer is 0.

Department 8 by Department 8 , 27, Israel

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1 solution

Department 8
Aug 12, 2015

We have 3 − tan ⁡ 2 1 2 × . . . . . . × 3 − tan ⁡ 2 60 2 × . . . . . . × 3 − tan ⁡ 2 360 2 \frac { 3-\tan ^{ 2 }{ 1 } }{ 2 } \times ......\times \frac { 3-\tan ^{ 2 }{ 60 } }{ 2 } \times ......\times \frac { 3-\tan ^{ 2 }{ 360 } }{ 2 } .

We know tan ⁡ 2 60 = 3 \tan^{2}{60} = 3 , therefore the above given equation becomes 0 \boxed{0}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

(OMG... you've got to be kidding.... I was even thinking of using complex numbers when i gave up ) Completely fooled me... nice question though.

Jeffrey Li - 5 years, 10 months ago

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