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

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

2. Rosh007

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

3. Rosh007

***write nor right

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

And then i cancelled the cos(x)

6. Rosh007

yup good

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

8. Rosh007

now can you write what answer you got

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

So i wrote pi/3 and 2pi/3

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

12. Rosh007

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

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

14. Rosh007

How you got 2pi/3

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

16. Rosh007

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?

is it pi/3?

18. Rosh007

yup it is

But i need to state all the values for it

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

How can i write this as a general solution

22. Rosh007

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

23. Rosh007

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

Oo i think i found it

Is it pi/3 + 2kpi

and 2pi/3 + 2kpi

27. Rosh007

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

And one more thing

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

30. Rosh007

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

31. Rosh007

** can

32. Rosh007

No same one

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

35. Rosh007

am I clear?

36. Rosh007

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. Rosh007