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Question

The solution set of x+y=2π3 and cosx+cosy=32 where x and y are real is

A
ϕ (empty)
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B
1
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C
2
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D
3
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Solution

The correct option is A ϕ (empty)
Given x+y=2π3 and cosx+cosy=32

y=(2π3x)

cosx+cos(2π3x)=32

cosx+(12cosx+32sinx)=32

12cosx+32sinx=32

sinπ6cosx+cosπ6sinx=32

sin(x+π6)=32=1.5 [sin(A+B)=sinAcosB+sinBcosA]

Which is never possible as 1sinθ1 but here sin(x+π6)=1.5

Hence, no solution exists

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