How would I go about simplifying some of these trigonometric problems?

1. (tanx / cotx) + 1

2. (1-2cos^(x) / (2sinxcosx)

3. 1 - (sin^2(x)) / (1+cosx)

4. sin^2(x) * sec^2(X) * csc^2(x) * cos^2(x)

5.sinx * secx

6. (1-sin^2(x) * (1+tan^2(x)

7. (1-cosx) * (1+secx) * cotx

8. (csc^2(x)) * (1-cos^2(x))

9. (sinx / cscx) + (cosx / secx)

10. (1 / 1-sinx) / (1 / 1+sinx)

lastly, 11. tan^2(x) * csc^2(x) * cot^2(x) * sin^2(x)

I would appreciate if you included how you simplified the question.

Thanks,

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2 Answers

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  • 1 decade ago
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    11. tan^2(x) * csc^2(x) * cot^2(x) * sin^2(x)

    Because cot^2(x)=1/tan^2(x) and

    csc^2(x)=1/sin^2(x), the answer is simply 1

  • 1 decade ago

    We could be here all day simplifying all 11. It sounds to me like you are too lazy to do it yourself.

    All you have to remember is

    tan=sin/cos

    cot=cos/sin or 1/tan

    sec=1/cos

    csc=1/sin

    cos^2x+sin^2x=1

    1+tan^2x=sec^2x

    1+cot^2x=csc^2x

    Then if you have 2 fractions divided by each other, like you will in the first problem, then the second fraction gets flipped and you times it by the first.

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