If cos x = tan y, cot y = tan z and cot z = tan x, then sin x is equal to

If cos x = tan y, cot y = tan z and cot z = tan x, then sin x is equal to

  1. A

    5+14

  2. B

    5-14

  3. C

    5+12

  4. D

    5-12

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    Solution:

    Given ,cos x = tan y, cot y = tan z and cot z = tan x

            cosx=tany    cosx=1tanz        cosx=cotzcosx=tanx        cosx=sinx/cosxcos2x=sinx        1sin2x=sinxsin2x+sinx1=0        sinx=1±14×(1)2×1=1±52        sinx=512       152<1 

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