anonymous 3 years ago Find the real values of x for which the equation is valid.

1. anonymous

$2\cos (x)=\sqrt{3}\cot (x)$

2. anonymous

can you right cot (x) in terms of sin and cos

3. anonymous

***write nor right

4. anonymous

I wrote cot(x)=cos(x)/sin(x)

5. anonymous

And then i cancelled the cos(x)

6. anonymous

yup good

7. anonymous

And i was left with sin(x) = sqrt(3)/2

8. anonymous

now can you write what answer you got

9. anonymous

I then thought i can get infinite answers....

10. anonymous

So i wrote pi/3 and 2pi/3

11. anonymous

I think there are more solutions but i dont know how to writee them

12. anonymous

..... ok can you tell me what is th sin invers of $\sin^{-1}( \frac{ \sqrt{3} }{ 2 })$

13. anonymous

It is pi/3 and 2pi/3 between 0 and 2pi

14. anonymous

How you got 2pi/3

15. anonymous

I did pi - pi/3 because sin is also positive in that quadrant

16. anonymous

yes exactly.. so when we find inverse if get more values we take the lesser value usually.. for example 7pi/3 is also giving same answer but by using the concept above answer will b what?

17. anonymous

is it pi/3?

18. anonymous

yup it is

19. anonymous

But i need to state all the values for it

20. anonymous

so i need to write, pi/3, 2pi/3, 7pi/3, 8pi/3, 13pi/3, 14pi/3 .......

21. anonymous

How can i write this as a general solution

22. anonymous

ok.. first take a look at pi/3 and 7pi/3 what can you find

23. anonymous

any similarity?.. or relation... (clue can you relate with multiple of 2pi

24. anonymous

Oo i think i found it

25. anonymous

Is it pi/3 + 2kpi

26. anonymous

and 2pi/3 + 2kpi

27. anonymous

exactly.. ther you go... what is k...( no need to tll if you ar pretty sure)

28. anonymous

And one more thing

29. anonymous

Will i also need to evaluate cos(x)=0?

30. anonymous

??? not clear... cab you make it more clear?is it another question?

31. anonymous

** can

32. anonymous

33. anonymous

No same one

34. anonymous

wouldn't 2cos(x) = sqrt(3)cot(x) if cos(x) = 0 also

35. anonymous

am I clear?

36. anonymous

ok...... asuming a fuction itself is zero may not lad you to corrct ansewr... also... here the cos (x) cancels each other (ofcourse before assuming it zero) hence assuming cos (x) = 0 is wrong..

37. anonymous