Jika cos x=akar(5)/5 maka cot (pi/2-x)=...

cot (pi/2-x) = tan x = +/- 2

Pembahasan

Untuk mencari nilai \(cot(\frac{\pi}{2} - x)\) ketika \(cos x = \frac{\sqrt{5}}{5}\), kita dapat menggunakan identitas trigonometri \(cot(\frac{\pi}{2} - x) = tan x\). 

Pertama, kita perlu mencari nilai \(sin x\). Kita tahu bahwa \(sin^2 x + cos^2 x = 1\). 
Maka, \(sin^2 x = 1 - cos^2 x\) 
\(sin^2 x = 1 - (\frac{\sqrt{5}}{5})^2\) 
\(sin^2 x = 1 - \frac{5}{25}\) 
\(sin^2 x = 1 - \frac{1}{5}\) 
\(sin^2 x = \frac{4}{5}\) 
\(sin x = \pm \frac{2}{\sqrt{5}} = \pm \frac{2\sqrt{5}}{5}\). 

Karena \(cot(\frac{\pi}{2} - x) = tan x = \frac{sin x}{cos x}\), maka:
\(tan x = \frac{\pm \frac{2\sqrt{5}}{5}}{\frac{\sqrt{5}}{5}}\)
\(tan x = \pm 2\).

Jadi, \(cot(\frac{\pi}{2} - x) = \pm 2\).