Math, asked by cnuseena9095, 10 months ago

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

Answers

Answered by MaheswariS
3

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}

Answered by StaceeLichtenstein
0

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

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