JEE Main & Advanced Sample Paper JEE Main - Mock Test - 23

  • question_answer
    If \[{{(tanx-tany)}^{2}},{{(any-tanz)}^{2}}\]and\[{{(tanz-tanx)}^{2}}\] are in A.P, then \[(tanx-tany),\]\[(tany-tanz)\]and\[(tanz-tanx)\]are in

    A) A.P.                 

    B) G.P.

    C) H.P.           

    D) None of these

    Correct Answer: C

    Solution :

    [c] : Let \[a=\tan x-\tan y,b=\tan y-\tan z\]and \[c=\tan z-\tan x\] \[\therefore \]a + b + c = 0                                            ...(i) From (i), \[{{b}^{2}}={{a}^{2}}+{{c}^{2}}+2ac\]                          ...(ii) According to question, \[2{{b}^{2}}={{a}^{2}}+{{c}^{2}}\] \[\Rightarrow \]\[2{{b}^{2}}={{b}^{2}}-2ac\]              [Using (ii)] \[\Rightarrow \]\[-{{b}^{2}}=2ac\] \[\Rightarrow \]\[-b=\frac{2ac}{b}=\frac{2ac}{-(a+c)}\Rightarrow b=\frac{2ac}{a+c}\] \[\therefore \]a, b, c are in H.P.

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