Question

Sendo cos x=1/4 sendo 0<x<$\pi$/2. Calcule tg x
 

Answer 1

cos²x + sen²x = 1
(1/4)² + sen²x = 1
1/16 + sen²x = 1
1 + 16sen²x = 16
16sen²x = 15
sen²x = 15 / 16
senx = √15  / 4

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tgx = senx / cosx 
tgx = √15  / 4 / 1 / 4
tgx = √15 / 4 . 4
tgx = √15