## anonymous one year ago can somebody please help me with this question? i am completely lost. Use basic identities to simplify the expression. (picture below)

1. anonymous

2. SolomonZelman

$$\large\color{black}{ \displaystyle \frac{ \cos^2\theta}{\sin^2\theta}+\csc\theta\sin\theta }$$

3. SolomonZelman

some basic identities: $$\large \color{black}{\sin\theta\csc\theta=1}$$ $$\large \color{black}{\cos\theta\sec\theta=1}$$ $$\large \color{black}{\tan\theta\cot\theta=1}$$

4. SolomonZelman

i still want to ask, do you have any options?

5. anonymous

these are my options

6. SolomonZelman

ok, then you need 2 more rules" $$\color{black}{\large \dfrac{\sin\theta}{\cos\theta}=\tan\theta}$$ $$\large \color{black}{\tan^2\theta+1=\sec^2\theta}$$

7. SolomonZelman

well, the first rule also applies when sine and cosine are raised to any power of n, such that: $$\color{black}{\large \dfrac{\sin^n\theta}{\cos^n\theta}=\tan^n\theta}$$ (for all n, of course)

8. Nnesha

or maybe u need 2 More rules :3 Mo$\huge\rm \frac{ \cos \theta }{ \sin \theta}= \cot \theta$ $\huge\rm cot^2 \theta +1=\csc^2\theta$

9. SolomonZelman

oh, Nnesha, you are right, because it is cosine/sine, not the other way around as I thought for some reason:) and thus, the 2nd rule you posted comes about.

10. anonymous

so, what exactly do i do with the rules you guys gave me?

11. SolomonZelman

$$\LARGE \color{blue}{\unicode{x10009999999}}$$$$\LARGE \color{blue}{\unicode{x120D999}}$$$$\LARGE \color{blue}{\unicode{x3D5}}$$$$\LARGE \color{blue}{\unicode{x8594}}$$ $$\LARGE \color{blue}{:)}$$

12. SolomonZelman

u apply them to your problem

13. SolomonZelman

$$\large\color{black}{ \displaystyle \frac{ \cos^2\theta}{\sin^2\theta}+\csc\theta\sin\theta }$$ apply to the second term, one of the rules that I posted in the very beginning.

14. anonymous

okay what i think i understand is cos^2(theta) / sin^2(theta) = 1

15. anonymous

then cos/sin = cot

16. anonymous

would it then be cot^2(theta) = 1 ?

17. Nnesha

nope.

18. Nnesha

cos^2/sin^2 is not equal to one if cos /sin =cot then cos^2 / sin^2 = cot^2

19. anonymous

cot^2 (theta) + 1 ?

20. Nnesha

yes right cot^2 theta +1 which is e qual to what ?

21. anonymous

csc^2 (theta) ?

22. Nnesha

yep right

23. anonymous

thank you so much!

24. Nnesha

my pleasure