Question

General solution of the equation cot 3 theta minus cot theta equal to zero

Answer 1

Answer:

The solution is

$\theta=\frac{n\pi}{2},\:n\in\,Z}$

Step-by-step explanation:

$\text{Given:}$

$cot3\theta=cot\theta$

$\implies\frac{cos3\theta}{sin3\theta}=\frac{cos\theta}{sin\theta}$

$\implies\,sin\theta\,cos3\theta=cos\theta\sin3\theta$

$\implies\,sin\theta\,cos3\theta-cos\theta\,sin3\theta=0$

Using

$\boxed{sin(A-B)=sinA\,cosB-cosA\,sinB}$

$\implies\,sin(\theta-3\theta)=0$

$\implies\,sin(-2\theta)=0$

$\implies\,-sin2\theta=0$

$\implies\,sin2\theta=0$

Using

$\boxed{\text{The solution of }\bf\,sin\theta=0\text{ is }\bf\theta=n\,\pi,\:n\in\,Z}$

$\implies\,2\theta=n\pi,n\in\,Z$

$\implies\,\boxed{\bf\theta=\frac{n\pi}{2},\:n\in\,Z}$

Answer 2

Given

Cot3θ-cotθ=0

To find:

General solution of the equation

Solution :

As mention in the question

Cot3θ-cotθ=0

Cot3θ = cotθ

1/tan3θ =1/tanθ

tanθ=tan3θ

tan(nπ + θ)=tan3θ---------eq(1)

As we know that

tan(nπ + θ)=tanθ

from the eq(1)

(nπ + θ)=3θ

θ=(nπ + θ)/3