anonymous
  • anonymous
Find the real values of x for which the equation is valid.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[2\cos (x)=\sqrt{3}\cot (x)\]
anonymous
  • anonymous
can you right cot (x) in terms of sin and cos
anonymous
  • anonymous
***write nor right

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anonymous
  • anonymous
I wrote cot(x)=cos(x)/sin(x)
anonymous
  • anonymous
And then i cancelled the cos(x)
anonymous
  • anonymous
yup good
anonymous
  • anonymous
And i was left with sin(x) = sqrt(3)/2
anonymous
  • anonymous
now can you write what answer you got
anonymous
  • anonymous
I then thought i can get infinite answers....
anonymous
  • anonymous
So i wrote pi/3 and 2pi/3
anonymous
  • anonymous
I think there are more solutions but i dont know how to writee them
anonymous
  • anonymous
..... ok can you tell me what is th sin invers of \[\sin^{-1}( \frac{ \sqrt{3} }{ 2 })\]
anonymous
  • anonymous
It is pi/3 and 2pi/3 between 0 and 2pi
anonymous
  • anonymous
How you got 2pi/3
anonymous
  • anonymous
I did pi - pi/3 because sin is also positive in that quadrant
anonymous
  • 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?
anonymous
  • anonymous
is it pi/3?
anonymous
  • anonymous
yup it is
anonymous
  • anonymous
But i need to state all the values for it
anonymous
  • anonymous
so i need to write, pi/3, 2pi/3, 7pi/3, 8pi/3, 13pi/3, 14pi/3 .......
anonymous
  • anonymous
How can i write this as a general solution
anonymous
  • anonymous
ok.. first take a look at pi/3 and 7pi/3 what can you find
anonymous
  • anonymous
any similarity?.. or relation... (clue can you relate with multiple of 2pi
anonymous
  • anonymous
Oo i think i found it
anonymous
  • anonymous
Is it pi/3 + 2kpi
anonymous
  • anonymous
and 2pi/3 + 2kpi
anonymous
  • anonymous
exactly.. ther you go... what is k...( no need to tll if you ar pretty sure)
anonymous
  • anonymous
And one more thing
anonymous
  • anonymous
Will i also need to evaluate cos(x)=0?
anonymous
  • anonymous
??? not clear... cab you make it more clear?is it another question?
anonymous
  • anonymous
** can
anonymous
  • anonymous
if it is another qustion your answer is (2k+1)pi/2
anonymous
  • anonymous
No same one
anonymous
  • anonymous
wouldn't 2cos(x) = sqrt(3)cot(x) if cos(x) = 0 also
anonymous
  • anonymous
am I clear?
anonymous
  • 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..
anonymous
  • anonymous
**lead you to correct answer

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