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Math Help - Trig simplification issues

  1. #1
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    Unhappy Trig simplification issues

    I'v been sick in my college math class and have been a bit behind. I really could use some help and have been slamming my head against my text book trying to figure some of these simplifications out. One in particular that's been driving me nuts is this.

    cosx/(((cosx-1)/(cosx))-1) Sorry for my overuse of parentheses here not sure how to make it look all professional.

    another is
    if Asin(squared)x+Bcos(squared)x =1 show that
    sin(squared)x=(1-b)/a-b) and tan(squared)x=(b-1)/(1-a)

    my last one is
    suppose Asinx+cosx=1 and bsinx-cosx=1 show that AB=1

    any help you can offer would be much appreciated as I've been working on these problems for hours and solved nothing.
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  2. #2
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    Hello, abzolutezero!

    Here's the third one . . .


    \text{Suppose: }\:\begin{Bmatrix}A\sin x+\cos x &=& 1 & [1] \\ B\sin x-\cos x &=& 1 & [2] \end{Bmatrix}

    \text{Show that: }\:AB\:=\:1

    From [1], we have: . A \;=\;\dfrac{1-\cos x}{\sin x}\;\;[3]

    From [2], we have: . B \;=\;\dfrac{1+\cos x}{\sin x}\;\;[4]


    Multiply [3] and [4]:

    . . \displaystyle A\cdot B \;=\;\frac{1-\cos x}{\sin x}\cdot\frac{1+\cos x}{\sin x} \;=\; \frac{1-\cos^2\!x}{\sin^2\!x} \;=\;\frac{\sin^2\!x}{\sin^2\!x} \;=\;1
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  3. #3
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    Quote Originally Posted by abzolutezero View Post
    cosx/(((cosx-1)/(cosx))-1)


    if Asin(squared)x+Bcos(squared)x =1 show that
    sin(squared)x=(1-b)/a-b) and tan(squared)x=(b-1)/(1-a)
    if this is what you meant for the fist problem ...

    \displaystyle \frac{\cos{x}}{\frac{\cos{x}-1}{\cos{x}}-1}

    ... multiply numerator and denominator by \cos{x} , then simplify.



    for the second problem(s), I assume the cap A's and B's are the same as the lower case ones ...

    a\sin^2{x} + b\cos^2{x} = 1

    a\sin^2{x} + b(1-\sin^2{x}) = 1

    distribute b , then solve for \sin^2{x}.



    a\sin^2{x} + b\cos^2{x} = 1

    a\sin^2{x} + b\cos^2{x} = \sin^2{x} + \cos^2{x}<br />

    a\sin^2{x} - \sin^2{x} = \cos^2{x} - b\cos^2{x}<br />

    \sin^2{x}(a - 1) = \cos^2{x}(1 - b)

    \frac{\sin^2{x}}{\cos^2{x}} = \frac{1-b}{a-1}<br />

    \tan^2{x} = \frac{1-b}{a-1} = \frac{b-1}{1-a}
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