## anonymous one year ago Trig/ Pre Cal/identies Am I on the right path? Please do not give answer but guide me. Thank you. The problem $\frac{1}{\sin x + 1} + \frac{1}{\csc x +1}$ $\frac{\csc x + 1 + \sin x + 1}{( \sin x + 1)( \csc x + 1)}$ Am I on the right path?

1. anonymous

it should be $\frac{1}{\sin x + 1} + \frac{1}{\csc x +1} = 1$ $\frac{\csc x + 1 + \sin x + 1}{( \sin x + 1)( \csc x + 1)} = 1$

2. Nnesha

well first write csc in terms of sin :-) that will be easy :-)

3. Nnesha

$\frac{1}{\sin x + 1} + \frac{1}{\rm \color{reD}{\frac{1}{sinx} +1}} = 1$ like this solve red part first

4. anonymous

So $\frac{\frac{1}{sin x} x + 1 + \sin x + 1}{( \sin x + 1)( \frac{1}{sin x} x + 1)}$

5. Nnesha

better to gget rid of fraction first :-)

6. anonymous

so do I times the numerator and denominator by sin??

7. Nnesha

$\frac{1}{\sin x + 1} + \frac{1}{\rm \color{reD}{\frac{1}{sinx} +1}} = 1$ $\large\rm \color{reD}{\frac{ 1 }{ \sin x } +1}$ multiply by sinx/1 do you know how to find common denominator ? just for the red part

8. anonymous

For the red part the common denominator is sin x and 1. For the red we have $1+ \sin x$ corect?

9. Nnesha

for the red part |dw:1434223526447:dw| common denominator is sin x

10. anonymous

yes correct. I forgot to include the denominator

11. Nnesha

in other words multiply by sinx/1 |dw:1434223578712:dw| let me know if you have any question :-)

12. anonymous

Got it

13. Nnesha

alright move on

14. Nnesha

$\huge\rm \frac{1}{\sin x + 1} + \frac{1}{\rm \color{reD}{\frac{1 + sinx }{sinx} }} = 1$ now change divison to multiplication $\huge\rm \frac{ 1 }{ \frac{ 1+sinx }{ sinx } }$ multiply top with the reciprocal of the bottom fraction

15. Nnesha

for example $\large\rm \frac{ a }{ \frac{ b }{ c } } = a \times \frac{ c }{ b }$

16. anonymous

so is it $$\frac{1}{1}$$

17. anonymous

so $$\frac{sin }{1+ sin x}$$

18. Nnesha

yes right :-)

19. Nnesha

$\huge\rm \frac{1}{\sin x + 1} + \frac{sin x}{\rm \color{reD}{ sinx +1 }} = 1$ 1 + sinx is same as sinx +1

20. anonymous

so we have $\frac{sin x}{sinx + 1} = 1$ but that does not equal 1]

21. Nnesha

check numerator again that's not right

22. anonymous

I see... Right in front of my face... lol man these things make me see crosseye

23. anonymous

so we have $\frac{1+sin x}{sinx + 1}\ = 1 but that does not equal 1] 24. Nnesha why not ?? 25. anonymous so we have \[ \frac{1+sin x}{sinx + 1} = 1$

26. Nnesha

1+ sin x is same as sinx+1

27. anonymous

That post before my last post was from me copying and pasting and I did not take the last part out.

28. anonymous

Thank you. I was working it all types of ways but all I had to do was work the bottom denominator . Thank you!!

29. Nnesha

my pleasure :-) gO_od job!! :-)