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Vijay Butala
Asked: 2022-11-01T19:06:32+05:30 In:

If `x+y=2pi//3` and `sin x//sin y=2`, then the
A. number of values of `x in [0, 4pi]` are 4
B. number of values of `x in [0, 4pi]` are 2
C. number of values of `y in [0, 4pi]` are 4
D. number of values of `y in [0, 4pi]` are 8

If `x+y=2pi//3` and `sin x//sin y=2`, then the
A. number of values of `x in [0, 4pi]` are 4
B. number of values of `x in [0, 4pi]` are 2
C. number of values of `y in [0, 4pi]` are 4
D. number of values of `y in [0, 4pi]` are 8
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  1. Correct Answer – A::C
    `x+y=2pi//3` or `y=(2pi//3)-x`
    `:. sin x=2 sin ((2pi)/3-x)`
    `=2[(sqrt(3)/2)cos x+(1/2) sin x]`
    `=sqrt(3) cos x + sin x`
    `rArr cos x =0`
    `rArr x=npi+pi/2, n in Z`
    `rArr y=(2pi)/3- n pi-pi/2=pi/6-n pi`
    Hence, for `x in [0, 4pi], x=pi//2, 3pi//2, 5pi//2, 7pi//2` and for `y in [0, 4pi], y=pi//6, 7pi//6, 13pi//6, 19pi//6`

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