Such a beauty

Geometry Level 1

if 4 n x = π 4nx = \pi

then ( t a n x ) ( t a n 2 x ) ( t a n 3 x ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( t a n ( 2 n − 1 ) x ) (tanx)(tan2x)(tan3x) ................................(tan(2n -1)x)


The answer is 1.

U Z by U Z , 24, Guyana

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1 solution

U Z
Oct 23, 2014

2 n x − x = π 2 − x 2nx - x = \frac{\pi}{2} - x

( 2 n − 1 ) x = π 2 − x (2n - 1)x = \frac{\pi}{2} - x

t a n ( 2 n − 1 ) x = c o t x tan( 2n -1)x = cotx

thus

t a n ( 2 n − 1 ) x ( t a n x ) = 1 tan( 2n -1)x(tanx)=1

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