InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `sinx+siny=sqrt(3)(cos y-cos x),`then `sin3x+sin3y=`(a)`2sin3x`(b) 0 (c) 1 (d) none of these |
|
Answer» `sinx+siny = sqrt3(cosy-cosx)` `=>2sin((x+y)/2)cos((x-y)/2)= sqrt3(2sin((x+y)/2)sin((x-y)/2)) ` `=>sin((x+y)/2)cos((x-y)/2) - sqrt3sin((x+y)/2)sin((x-y)/2) = 0` `=>sin((x+y)/2)[cos((x-y)/2) - sqrt3sin((x-y)/2)] = 0` `=>sin((x+y)/2) = 0 or cos((x-y)/2) - sqrt3sin((x-y)/2) = 0` `=>x+y = 0 or cot ((x-y)/2) = sqrt3` `=>x = -y or (x-y)/2 = pi/6` `=>x= -y or x = y+pi/3` When `x = -y,` `sin3x+siny = sin(-3y)+sin3y = sin3y-sin3y= 0` When, `x = y+pi/3,` `sin3x+siny = sin3(y+pi/3)+sin3y = sin(pi+3y)+sin3y= -sin3y+sin3y = 0` `:.` In both cases, ` sin3x+sin3y = 0.` |
|