## anonymous one year ago simplify the expression

1. anonymous

$\frac{ (1-\cot(x))^{2} }{ \cot(x) }$

2. anonymous

@mathstudent55

3. anonymous

@carolinar7

4. anonymous

@pooja195, @Australopithecus

5. Australopithecus

http://www.sosmath.com/trig/Trig5/trig5/trig5.html Here is a list of trig identities, just use them to simplify it. As for (1-cot(x))^2 you can expand it, then cancel out terms

6. anonymous

it doesnt help me

7. Australopithecus

have you tried expanding (1-cot(x))^2 ??

8. Australopithecus

show me the work you have done so far

9. anonymous

yeah it wasnt working out for me

10. anonymous

i dont know how to put up work

11. Australopithecus

Expansion rule: (a+b)^2 = (a+b)(a+b) = a*a + a*b + b*a + b*b = a^2 + 2ab + b^2

12. Australopithecus

13. anonymous

|dw:1438196219013:dw|

14. Australopithecus

so you have: $\frac{1^2+\cot(x)*1+\cot^2(x)}{\cot(x)}$ looks good to me simplified you have: $\frac{1+\cot(x)+\cot^2(x)}{\cot(x)}$ Now next step you need to apply the fraction addition rule: $\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$ Note: you can only apply this rule when the denominator is the same.

15. Australopithecus

apply the rule and show me what you get

16. Australopithecus

17. Australopithecus

you messed up and misplaced a negative in your expansion

18. welshfella

= 1 - 2 cotx + cot ^ x ---------------- cot x divide each term by cot x note 1 / cot x = tan x

19. Australopithecus

remember you have: (1-cot(x))^2 so you need to do the following |dw:1438196628184:dw|

20. anonymous

so would it be cot(x)+2/

21. Australopithecus

Note: - * - = + - * + = - + * - = - + * + = +

22. welshfella

( a - b)^2 = a^2 - 2ab + b^2

23. Australopithecus

so writing it all out you have: 1*1 + 1*(-cos(x)) + 1*(-cos(x)) + (-cos(x))*(-cos(x))

24. Australopithecus

this isnt something you want to just memorize formulas for you should know the process of solving an expansion

25. anonymous

so would it be sin(x)cos(x)-2?

26. Australopithecus

So for example: (a + b)(c + d) ^ | first step start with a multiply it by c then multiply it by d you get a*c + a*d Now switch to b (a + b)(c + d) ^ | second step multiply b by c then multiply b by d then you get: a*c + a*d + b*c + b*d as for the next step once you have your problem split it into separate fractions makes it easier to visualize: $\frac{1 - 2\cot(x) + \cot(x)^2}{\cot(x)} = \frac{1}{\cot(x)} - \frac{2\cot(x)}{\cot(x)} + \frac{\cot^2(x)}{\cot(x)}$

27. Australopithecus

By rule: $a^{1} = a$ $\frac{1}{a} = a^{-1}$ and $a^{0} = 1$ Thus: $\frac{a}{a} = a^{1}a^{-1} = a^{1 + (-1)} = a^{0} = 1$

28. Australopithecus

so if you had: $\frac{\sin(x)}{\sin^2(x)} = \sin^1(x)*\sin^{-2}(x) = \sin^{1-2}(x) = \sin^{-1}(x) = \frac{1}{\sin(x)}$