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Question

If cosx+cos(k+x)cos(kx)=2 has real solutions, then

A
k[nπ+π3,nπ+2π3]
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B
k[2nπ+π3,2nπ2π3]
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C
k[nππ6,nπ+π6]
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D
k[2nππ6,2nπ+π6]
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Solution

The correct option is A k[nπ+π3,nπ+2π3]
cosx+cos(k+x)cos(kx)=2cosx2 sinksinx=2

We know that for an equation acosx+bsinx=c to have solution |c|a2+b2

1+4sin2k21+4sin2k4|sink|32sink32 or sink32k[2nπ+π3,2nπ+2π3] or k[(2n+1)π+π3,(2n+1)π+2π3]k[nπ+π3,nπ+2π3]

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