Question

What is the general solution for tan x + cot 3x =0

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$x=(2n+1)\frac{\pi }{4}, where,n=0,1,2....$

Step-by-step explanation:

In the given equation,

$tanx+cot3x=0\\\frac{sinx}{cosx}+\frac{cos3x}{sin3x} =0\\So,\\\frac{sinx.sin3x+cosx.cos3x}{sin3x.cosx}=0\\ As,\\sinA.sinB+cosA.cosB=cos(A-B)\\So,\\cos(3x-x)=0\\cos2x=0$

Now,

We know that the general solution of the cosx is provided by,

$cosx=\alpha\\So,\\x=(2n+1)\alpha$

Therefore, here we can say that,

The value of,

$\alpha=\frac{\pi}{2}</p><p>[tex]cos2x=0\\2x=(2n+1)\frac{\pi}{2} \\So,\\x=(2n+1)\frac{\pi}{4}$

Therefore, the correct form is $x=(2n+1)\frac{\pi }{4}, where,n=0,1,2....$