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If sin(x-y)=cos(x+y)=1/2,then the values of x and y lying b/w 0° and 180° are given by a.x=45°,y=45° b.x=45°,y=135° c.x=165°,y=15° d.x=165°,y=135°

If sin(x-y)=cos(x+y)=1/2,then the values of x and y lying b/w 0° and 180° are given by


a.x=45°,y=45°


b.x=45°,y=135°


c.x=165°,y=15°


d.x=165°,y=135°

Grade:12th Pass

3 Answers

Chetan Mandayam Nayakar
312 Points
12 years ago

x-y=nπ+ (-1)nsin-1(1/2), x+y=2mπ±cos-1(1/2), n and m are both integers

Krishna Pradyumna Mokshagundam
31 Points
12 years ago

it is d. x=165,y=135

Ashwin Muralidharan IIT Madras
290 Points
12 years ago

Hi Menka,

 

To solve this question quickly, first note that 0 <= x,y <= 180.

 

So min (x-y) = -180, and max (x-y) = 180

and min (x+y) = 0 and max (x+y) = 360

 

This is the interval where you need to be looking for solutions:

so x-y = 30 or 150

and x+y = 60 or 300.

 

Clearly only option D satisfies.

 

Hope that helps.

 

All the best,

Regards,

Ashwin (IIT Madras).

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