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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

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

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?

**lead you to correct answer