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Question

If tanxy2,tanz,tanx+y2 are in G.P., then show that cosx=cosy.cos2z

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Solution

b2=acsin2zcos2z=sinx+y2sinxy2cosx+y2cosxy2
sin2zcos2z=cosycosxcosy+cosx
cross multiply or by C and D
cosx.1=cosy(cos2zsin2z)=cosycos2z
Hence proved.

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