## anonymous one year ago Use basic identities to simplify the expression. cosecant of theta times cotangent of theta divided by secant of theta.

1. anonymous

write everything in terms of sine and cosine and see what cancels

2. anonymous

$$\huge \frac{\csc \theta \times \cot \theta}{\sec \theta}$$ This is what we are working with correct?

3. anonymous

These things can get tricky but they are fun, when you are not being timed to do them lol

4. anonymous

Haha yeah and that is what the question is :)

5. DecentNabeel

@Nixy cot=cos/sin not sin/cos

6. anonymous

opps yep thanks for the catch

7. anonymous

$$\huge \frac{\frac{1}{\sin \theta} \times \frac{cos}{sin}}{\sec \theta}$$ now work the top

8. anonymous

Uhhh this is bad, I don't know how to....sorry I am taking this online and my teacher isn't that helpful :(

9. DecentNabeel

$\mathrm{Simplify}\:\frac{\frac{1}{\sin \left(θ\right)}\cdot \frac{\sin \left(θ\right)}{\cos \left(θ\right)}}{\sec \left(θ\right)}:\quad 1$

10. anonymous

wait isn't it cos over sin?

11. anonymous

Yes, he made a boo boo too :-D

12. DecentNabeel

yes

13. anonymous

sec is 1/cos theta correct? so would I put that in?

14. DecentNabeel

yes

15. anonymous

and then cancel out the cos?

16. anonymous

@peachpi chime in any time to help :-) @peachpi is good at these. She/He has helped me on some before.

17. anonymous

Oh okay thanks :)

18. anonymous

you guys look like you have it under control

19. anonymous

write the denominator as 1/cos Θ. then flip it to the reciprocal when you change division to multiplication |dw:1435872610978:dw|

20. anonymous

nothing cancels but you can multiply straight across

21. anonymous

so it comes out to cot theta ^2?

22. anonymous

yes

23. anonymous

oh wow so I made it more complicated than it was

24. anonymous

yeah that happens a lot with these. I've done one on here where I basically went around in circles twice before getting to the solution

25. anonymous

Haha yeah oops my bad... anyways thank you so much to all of you!! I'll remember your usernames for sure because I'm sure I'll need help later on :)

26. anonymous

I think I made a boo boo

27. anonymous

yeah somewhere between the 5th and 6th steps

28. anonymous

@peachpi

29. anonymous

Nope still wrong... lol

30. LynFran

how about $\frac{ 1 }{ \sin \theta }*\frac{ \cos \Theta }{ \sin \Theta }/\sec$$\frac{ \cos \theta }{ \sin ^{2}\theta }*\cos$$\frac{ \cos ^{2}\theta }{ \sin ^{2}\theta }$$\cot ^{2}\theta$

31. anonymous

@LynFran is correct. @Nixy It looked like you were cancelling/dividing one part of the numerator but not the other

32. anonymous

I got what LynFran got

33. anonymous

$\huge \frac{\frac{1-sin^2}{sin^2 }}{1}$ $\huge \frac{\frac{cos^2}{sin^2 }}{1}$

34. anonymous

yeah that's it

35. anonymous

$\huge \frac{\frac{1}{\sin \theta} \times \frac{cos}{sin}}{\sec \theta}$ $\huge \frac{\frac{cos}{\sin^2}}{\sec \theta}$ $\huge \frac{\frac{cos}{\sin^2}}{\frac{1}{cos}}$ $\huge \frac{\frac{cos}{\sin^2}}{\frac{1}{cos}} \times cos$ $\huge \frac{\frac{cos^2}{\sin^2}}{\frac{1}{cos}} \times cos$ $\huge \frac{\frac{cos^2}{\sin^2}}{1}$ $\huge \frac{cos^2}{sin^2}$ $\huge \cot^2$

36. anonymous

These things are fun :-D