# 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,

Relevance

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

• 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.