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Question

If cos(xy),cosx,cos(x+y) are in H.P., where y2nπ,nZ, then the value of [cosxsecy2] is/are

(where [.] denotes greatest integer function)

A
2
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B
1
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C
0
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D
1
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Solution

The correct options are
A 2
D 1
cos(xy),cosx,cos(x+y) are in H.P.

cosx=2cos(xy)cos(x+y)cos(xy)+cos(x+y)cosx=2(cos2xsin2y)2cosxcosycos2xcosy=cos2xsin2ysin2y=cos2x(1cosy)1cos2y=cos2x(1cosy)(1cosy)(1+cosy)=cos2x(1cosy)1+cosy=cos2x(y2nπcosy1)cos2x=2cos2y2cos2xsec2y2=2cosxsecy2=±2[cosx×secy2]=[2] or [2][cosx×secy2]=1,2

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