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Shruti
Shruti asked in Science & MathematicsMathematics · 7 years ago

if a, b,c are in AP then tan A/2, tan B/2, tan C/2 are in?

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    Lv 6
    7 years ago
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    Let tan A/2, tan B/2, tan C/2 be in HP then

    2tan A/2tanC/2 = tan B/2 (tan A/2 + tan C/2) OR

    2SQRT[(s -- b)(s -- c)(s -- a)(s -- b)/(s -- a)(s -- c)s^2] = SQRT[(s -- c)(s -- a)(s -- b)(s -- c)/((s -- b)(s -- a)s^2] + SQRT[(s -- c)(s -- a)(s -- a)(s -- b)/(s -- b)(s --c)s^2] OR

    2(s -- b)/s = (s -- c)/s + (s -- a)/s giving

    2(s -- b) = (s -- c) + (s -- a) OR

    s -- a, s -- b, s -- c are in AP OR

    a, b, c are in AP

    so if a, b, c are in AP, tan A/2, tan B/2, tan C/2 are in HP ANSWER

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