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If Cos(x-y),Cos(x),Cos(x+y) are in HP, then 1+cos(y)=?
a)Cosx
b)Cos^2 (x)
c)Sinx
d)Sin^2 (x)
Plz explain..
Dear chilukari,
2/cosx =1/cos(x-y) + 1/cos(x+y)
2/cosx = 2cosxcosy/(cos2xcos2y-sin2xsin2y)-------1
change sin2y = 1-cos2y in eqution 1 we get
cos2y - cos2xcosy -sin2x=0
we can write above equation as cos2y-cosy+sin2xcosy-sin2x=0 writing cos2x=1-sin2x
and subsequently we write
cosy(cosy-1)+ sin2x(cosy-1)=0
(1-cosy)(cosy+sin2x)=0
so we get cosy = -sin2x
1+cosy =1-sin2x
1+cosy = cos2 x
so option b) is correct
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