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Find the real values of x for which the equation is valid.

Mathematics
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\[2\cos (x)=\sqrt{3}\cot (x)\]
can you right cot (x) in terms of sin and cos
***write nor right

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Other answers:

I wrote cot(x)=cos(x)/sin(x)
And then i cancelled the cos(x)
yup good
And i was left with sin(x) = sqrt(3)/2
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
..... 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
How you got 2pi/3
I did pi - pi/3 because sin is also positive in that quadrant
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?
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
ok.. first take a look at pi/3 and 7pi/3 what can you find
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
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?
??? not clear... cab you make it more clear?is it another question?
** can
if it is another qustion your answer is (2k+1)pi/2
No same one
wouldn't 2cos(x) = sqrt(3)cot(x) if cos(x) = 0 also
am I clear?
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..
**lead you to correct answer

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