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Let cosx + cosy = 1 , find the range of values of sinx − siny .

 Let cosx + cosy = 1, find the range of values of sinx − siny.

Grade:12th pass

2 Answers

Arun
25750 Points
4 years ago
Dear student 
 
cos x + cos y = 1
means two case
case1.
cos x= 1 and cos y = 0
hence sinx = 0 and siny = ± 1
hence sinx – sin y = ± 1
 
case2.
cosx = 0 and cosy = 1
hence sin x = ± 1 and sin y = 0
 
hence sinx – sin y = ± 1
 
Aditya Gupta
2081 Points
4 years ago
dear charu, the ans provided by arun is totally WRONG. the correct ans is below:
cosx + cosy = 1
sinx − siny = k
squaring and adding
k^2 + 1= cos^2x + cos^2y + 2cosxcosy + sin^2x + sin^2y – 2sinxsiny= 2 + 2cos(x+y)
or k= ± sqrt (1+2cos(x+y))
now, obviously k can be 0 when x= y= pi/3
also, cos(x+y) is less than equal to 1
or 2 cos(x+y) is less than equal to 2
or 1+2 cos(x+y) is less than equal to 1+2= 3
or sqrt (1+2 cos(x+y)) is less than equal to sqrt 3
or |k| is less than equal to sqrt 3
so, range of k is [–sqrt(3), sqrt(3)].
kindly approve :))

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