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Math Help - Please help me with my proving identities

  1. #1
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    Smile Please help me with my proving identities

    1. 1-sin x + 1-cos x = sin x + cos x-1
    cos x sin x sin x cos x

    2. sec^2x - tan^2 x + tan x = sin x + cos x
    sec x

    3. sin^3 x - sin x + cos x = cot x - cos^2 x
    sin x

    4. 1 + cot A + sec A _ tan A = sin A + cos A
    csc A
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by john edgar View Post
    1. 1-sin x + 1-cos x = sin x + cos x-1
    cos x sin x sin x cos x
    Hint: Multiply both sides of the equation by sin(x) cos(x) and then try it.

    Quote Originally Posted by john edgar View Post
    2. sec^2x - tan^2 x + tan x = sin x + cos x
    sec x
    Convert everything to sines and cosines:
    \frac{sec^2(x) - tan^2(x) + tan(x)}{sec(x)} = \frac{\frac{1}{cos^2(x)} - \frac{sin^2(x)}{cos^2(x)} + \frac{sin(x)}{cos(x)}}{\frac{1}{cos(x)}}

    = \frac{1}{cos(x)} - \frac{sin^2(x)}{cos(x)} + sin(x)
    Now add the fractions.

    Quote Originally Posted by john edgar View Post
    3. sin^3 x - sin x + cos x = cot x - cos^2 x
    sin x
    What's sin^2(x) - 1? Hint: It's a familiar identity that has been slightly rewritten.

    Quote Originally Posted by john edgar View Post
    4. 1 + cot A + sec A _ tan A = sin A + cos A
    csc A
    Convert everything to sines and cosines and simplify:
    \frac{1 + cot(A) + sec(A)}{csc(A)} - tan(A) = \frac{1 + \frac{cos(A)}{sin(A)} + \frac{1}{cos(A)}}{\frac{1}{sin(A)}} - \frac{sin(A)}{cos(A)}

    = sin(A) + cos(A) + \frac{sin(A)}{cos(A)} - \frac{sin(A)}{cos(A)}

    -Dan
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