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Question

# Match the following: lf cosx+cosy=a,sinx−siny=b then match the following.List-I List- II1. tan(x−y2) a.a2−b2a2+b2 2.sin(x−y) b.2aba2−b23. cos(x−y) c.b/a4. tan(x−y) d.2aba2+b2

A
1c,2a,3d,4b
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B
1b,2c,3a,4d
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C
1d,2a,3b,4c
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D
1a,2d,3b,4c
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Solution

## The correct option is A 1−c,2−a,3−d,4−bGiven cosx+cosy=a ⟹2cos(x+y2)cos(x−y2)=a⋯(1)sinx−siny=b⟹2cos(x+y2)sin(x−y2)=b⋯(2)(2)/(1)⟹2cos(x+y2)sin(x−y2)2cos(x+y2)cos(x−y2)=ba⟹tan(x−y2)=ba⋯(3)Let x−y=2t ⟹sin2t=2tant1+tan2t⟹sin(x−y)=2ba1+b2a2⟹sin(x−y)=2aba2+b2⟹cos2t=1−tan2t1+tan2t⟹cos(x−y)=1−b2a21+b2a2⟹cos(x−y)=a2−b2a2+b2⟹tan2t=sin2tcos2t⟹tan(x−y)=2aba2+b2a2−b2a2+b2⟹tan(x−y)=2aba2−b2

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