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Question

The general solution of equation 4cot2θ=cot2θtan2θ is

A
nπ±2π3,nϵz
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B
nπ±π3,nϵz
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C
nπ±π4,nϵz
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D
None of these
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Solution

The correct option is B nπ±π4,nϵz

Given, 4cot2θ=cot2θtan2θ
4(1tan2θ)tanθ=2(1tan2θ)
4tanθ4tan3θ=22tan4θ
tan4θ2tan3θ+2tanθ1=0
tanθ=1,1,1,1
tanθ=tanπ4 or tan3π4
θ=nπ±π4
θ=nπ±3π4

so,
LCM
θ=nπ±π4


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