1.

The number of pairs (x, y) satisfying the equations sin x + sin y = sin (x + y) and |x| + |y| = 1 is(a) 0(b) 2(c) 4(d) 6

Answer»

sin X + sin y = 2 sin [(x+y)/2]COS[(x-y)/2]

sin(x+y) = 2 sin [(x+y)/2]cos[(x+y)/2]

cos[(x-y)/2] = cos[(x+y)/2]

cos[(x-y)/2] - cos[(x+y)/2] =0

2sin(x/2)sin(y/2) = 0 [we converted difference of cosines into a product]

x=0 or y=0.

So, there are FOUR ANSWERS (0,1), (0,-1), (1,0), (-1,0).


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