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Q.

If 0<x,y<2π , the number of solutions of the system of equations sin⁡x sin⁡y=3/4  and cos⁡x cos⁡y=1/4 is 

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a

2

b

1

c

infinite 

d

0

answer is C.

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Detailed Solution

cos⁡(x−y)=1 ⇒ x−y=0   (Note  Note x−y≠2π)

⇒ x=y

cos⁡(x+y)=−1/2⇒x+y=120∘   or

240∘⇒x=y=60∘

or x=y=120∘ 

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If 0<x,y<2π , the number of solutions of the system of equations sin⁡x sin⁡y=3/4  and cos⁡x cos⁡y=1/4 is