Question

anyone know trigonometry by solving equations such as cot(3x)(cot(x) - 1) = 0

Answer 1

okay do you know trigonometric identities?

Answer 2

either cot 3x=0
\[\cot3x=0=\cot \left( 2n+1 \right)\frac{ \pi }{ 2 },n~is~an~integer.\]
\[3x=\left( 2n+1 \right) \frac{ \pi }{ 2 },x=?\]
or cotx-1=0
\[\cot x=1=\cot \left( n \pi+\frac{ \pi }{ 4 } \right),n~is~an~integer.\]
x=?

Answer 3

or more simplified way
\[\cot{3x}=0\]\[1/tan{3x}=0\]\[1=tan{3x}*0\]\[no~possible~solutions\]
\[\cot{x}-1=0\]\[\cot{x}=1\]\[\ 1/tan{x}=1\]\[\tan{x}=1\]\[\ x=tan^{-1}1\]\[x=45,225\]