Question

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

Answer 1

`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`