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How do you solve $cot^2x=2cotx-1$ ?

1 Answer

Jul 28, 2016

$x=Pin+pi/4$

Explanation:

$Cot^2(x)=2 cot(x)-1$

$cot^2(x)-2cot(x)+1=0$

It is quadratic equation in cot x

Use factorization to solve

$(cot(x)-1)(cot(x)-1)=0$
$(cot(x)-1)^2=0$

$cot(x)-1=0$

$cot (x)=1$ $( At x=pi/4 , cot (x)=1)$

$x=pi/4$

$x=Pin+pi/4$

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