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20 July, 21:26

Show that sinA - cosA + 1 / sinA + cosA - 1 = secA + tanA

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  1. 20 July, 22:20
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    sinA - cosA + 1 / sinA + cosA - 1 = secA + tanA

    Now secA = 1/cosA and tanA = sinA/cosA

    So sinA - cosA + 1 / sinA + cosA - 1 = 1/cosA + sinA / cosA

    From now on I'll write sinA = s and cosA = c : -

    (s - c + 1) / (s + c - 1) = 1/c + s/c

    (s - c + 1) / (s + c - 1) = (1 + s) / c

    Cross multiply:-

    s + c - 1 + s^2 + sc - s = sc - c^2 + c

    s^2 + c + sc - 1 = sc - c^2 + c

    s^2 - 1 + sc - sc + c - c = - c^2

    s^2 - 1 = - c^2

    - (1 - s^2) = - c^2

    Now 1 - s^2 = c^2 so:-

    - c^2 = - c^2

    So the identity is proved
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