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If tanx + tan 2x + root3 tanx tan 2x = root 3, Then ​a. x=(6n+1).pi/18 all n belongs to I ​b. x=(6n+1).pi/9 all n belongs to I ​c. x=(3n+1).pi/9 all n belongs to I I want answer with full solution.

If tanx + tan 2x + root3 tanx tan 2x = root 3, Then
 
​a. x=(6n+1).pi/18 all n belongs to I
​b. x=(6n+1).pi/9 all n belongs to I
​c. x=(3n+1).pi/9 all n belongs to I
 
I want answer with full solution.

Grade:11

1 Answers

Lab Bhattacharjee
121 Points
6 years ago
\tan x+\tan2x=\sqrt3(1-\tan x+\tan2x) \\ \implies\tan(x+2x)=\sqrt3=\tan\dfrac\pi3 \\3x=n\pi+\dfrac\pi3 \text{ where } n \text{ is any integer}

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