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Question

If sin1x+sin1y=2π3
and cos1xcos1y=π3
Then, (x,y) is equal to

A
(0,1)
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B
(12,1)
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C
(1,12)
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D
(32,1)
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Solution

The correct option is B (12,1)
We have,
sin1x+sin1y=2π3....(i)

cos1xcos1y=π3.....(ii)

(π2sin1x)(π2sin1y)=π3 ...... [sin1x+cos1x=π2]
sin1x+sin1y=π3.....(iii)
On adding Eqns. (i) and (iii), we get
sin1y=π2y=1
On subtracting Eq. (i) from Eq. (iii), we get
sin1x=π6x=12
(x,y)=(12,1).

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