## anonymous one year ago Which of the following world be an acceptable first step in simplifying the expression tanx/(1+secx)?

1. anonymous

2. jim_thompson5910

3. anonymous

I read through the notes like 10 times and still don't understand

4. jim_thompson5910

|dw:1440198581765:dw|

5. jim_thompson5910

|dw:1440198631242:dw|

6. anonymous

isn't it eliminating the denominator ?

7. jim_thompson5910

hint: think of the difference of squares formula

8. anonymous

the (b/2)^2 ?

9. jim_thompson5910

You've seen this formula before hopefully a^2 - b^2 = (a-b)(a+b)

10. anonymous

oh yeah. I'm used to the (a-b)2 but I know what you're talking about

11. anonymous

(a-b)^2 *

12. jim_thompson5910

so the idea is that we multiply top and bottom by 1-sec(x), then we get this |dw:1440198998954:dw|

13. jim_thompson5910

|dw:1440199030582:dw|

14. jim_thompson5910

|dw:1440199066043:dw|

15. jim_thompson5910

|dw:1440199086975:dw|

16. jim_thompson5910

what is 1-sec^2 equal to?

17. anonymous

umm , the first number to pop up in my head was 1 lol

18. jim_thompson5910

nope

19. jim_thompson5910

look at this identity sheet http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

20. jim_thompson5910

look on page 2 where it says "Pythagorean Identities"

21. anonymous

tan^2 theta ?

22. jim_thompson5910

yep

23. jim_thompson5910

|dw:1440199398015:dw|

24. jim_thompson5910

|dw:1440199419561:dw|

25. jim_thompson5910

so the original expression is equivalent to $\Large \frac{1-\sec(x)}{\tan(x)}$

26. anonymous

okay, so the answer would be a ?

27. jim_thompson5910

correct

28. anonymous

thank you!

29. jim_thompson5910

no problem