trig

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simplify the expression.

tan(π/2-x)tanx

  • trig -

    tan (pi/2 - x) = sin (pi/2 - x) / cos (pi/2 - x)

    But sin (pi/2 - x) = cos x

    and

    cos (pi/2 - x) = sin x

    <=>

    tan (pi/2 - x) = cos x / sin x = cotan x

    <=>

    tan (pi/2 - x) * tan x =

    cotan x * tan x =

    (cos x / sin x) * (sin x / cos x) =

    1

  • trig -

    works for me.

    the co-functions are the functions of the complementary angles. So, by definition, tan(π/2-x) = cot(x). Your proof works as well, though.

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