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Question

If tan x2=1-e1+e tan α2, then cos α=

(a) 1-e cos cos x+e

(b) 1+e cos xcos x-e

(c) 1-e cos xcos x-e

(d) cos x-e1-e cos x

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Solution

(d) cos x-e1-e cos x

Given: tanx2=1-e1+etanα2tanx2tanα2=1-e1+eSquaring both sides, we get,tan2x2tan2α2=1-e1+etan2α21-e=tan2x21+e

sin2α2cos2α21-e=sin2x2cos2x21+e121-cosα121+cosα1-e=121-cosx121+cosx1+e1-cosα1+cosx1-e=1+cosα1-cosx1+e1+cosx1-e-cosα1+cosx1-e=1-cosx1+e+cosα1-cosx1+ecosα1+cosx1-e+1-cosx1+e=1+cosx1-e-1-cosx1+ecosα=2cosx-2e2-2ecosx=cosx-e1-ecosx

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