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Math Help - More Expressions (Answer Verification Needed)

  1. #1
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    More Expressions (Answer Verification Needed)

    1. sin (x) (cos^2 (x)) - sin (x)
    My answer: -sin^3 (x)

    2. sin (x) + cot (x) (cos (x))
    My answer: csc (x)

    3. (sec^2 (x) - 1) / sec^2 (x)

    I only go to the part where its

    (tan^2 (x)) / 1 + tan^2 (x)

    i dont know what to do now..


    Thank you once again
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  2. #2
    Eater of Worlds
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    #3:

    You got it to \frac{tan^{2}x}{1+tan^{2}x}

    Use sin and cos:

    =\frac{\frac{sin^{2}x}{cos^{2}x}}{1+\frac{sin^{2}x  }{cos^{2}x}}

    =\frac{sin^{2}x}{cos^{2}x}\cdot\frac{cos^{2}x}{sin  ^{2}x+cos^{2}x}=sin^{2}x
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  3. #3
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    Hello, NeedHelp18!

    3)\;\;\frac{\sec^2\!x - 1}{\sec^2\!x}

    We have: . \frac{\sec^2\!x}{\sec^2\!x} - \frac{1}{\sec^2\!x} \;\;=\;\;1-\cos^2\!x \;\;=\;\;\sin^2\!x

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  4. #4
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    Thank you guys.

    did i get the other answers correct?
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by NeedHelp18 View Post
    1. sin (x) (cos^2 (x)) - sin (x)
    My answer: -sin^3 (x)

    2. sin (x) + cot (x) (cos (x))
    My answer: csc (x)

    3. (sec^2 (x) - 1) / sec^2 (x)

    I only go to the part where its

    (tan^2 (x)) / 1 + tan^2 (x)

    i dont know what to do now..


    Thank you once again

    Your answer to #1 is correct.

    I'm gonna verify your answer for #2:
    sin(x)+cot(x)cos(x)=sin(x)+\frac{cos(x)}{sin(x)}co  s(x)=sin(x)+\frac{cos^2(x)}{sin(x)}
    =\frac{1}{sin(x)}\cdot{\left(sin^2(x)+cos^2(x)\rig  ht)}=csc(x)
    It's good!

    But #3:

    \frac{tan^2(x)}{1+tan^2(x)}=\frac{tan^2(x)}{sec^2(  x)}=tan^2(x)cos^2(x)=sin^2(x).

    Hope that helped you out!!!
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