Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Write the expression in terms of sine and​ cosine, and then simplify so that no quotients appear in the final expression.?

(1+cot x)(1-tan x)

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  • Como
    Lv 7
    1 month ago

    :-

    ( 1 + cosx/sinx ) ( 1 - sinx/cosx )

    1 - sinx/cosx + cosx/sinx - 1

    - sin²x + cos²x

    ----------------------- = - tan x + cot x

    sin x cos x

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  • TomV
    Lv 7
    1 month ago

    (1+cot x)(1-tan x)

     = (1 + cos x/sin x)(1 - sin x/cos x)

     = (sin x + cos x)(cos x - sin x)/(sin x cos x)

     = (cos²x - sin²x)/(sin x cos x)

     = 2cos(2x)/sin(2x)

     = 2cot(2x)

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