## baddinlol Group Title Find the real values of x for which the equation is valid. one year ago one year ago

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

2. Rosh007 Group Title

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

3. Rosh007 Group Title

***write nor right

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

And then i cancelled the cos(x)

6. Rosh007 Group Title

yup good

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

8. Rosh007 Group Title

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 Group Title

..... 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 Group Title

How you got 2pi/3

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

16. Rosh007 Group Title

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 Group Title

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 Group Title

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

23. Rosh007 Group Title

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 Group Title

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 Group Title

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

31. Rosh007 Group Title

** can

32. Rosh007 Group Title

No same one

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

35. Rosh007 Group Title

am I clear?

36. Rosh007 Group Title

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 Group Title