Question

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

Answer 1

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

Answer 2

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

Answer 3

***write nor right

Answer 4

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

Answer 5

And then i cancelled the cos(x)

Answer 6

yup good

Answer 7

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

Answer 8

now can you write what answer you got

Answer 9

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

Answer 10

So i wrote pi/3 and 2pi/3

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

How you got 2pi/3

Answer 15

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

Answer 16

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?

Answer 17

is it pi/3?

Answer 18

yup it is

Answer 19

But i need to state all the values for it

Answer 20

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

Answer 21

How can i write this as a general solution

Answer 22

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

Answer 23

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

Answer 24

Oo i think i found it

Answer 25

Is it pi/3 + 2kpi

Answer 26

and 2pi/3 + 2kpi

Answer 27

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

Answer 28

And one more thing

Answer 29

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

Answer 30

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

Answer 31

** can

Answer 32

if it is another qustion your answer is (2k+1)pi/2

Answer 33

No same one

Answer 34

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

Answer 35

am I clear?

Answer 36

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..

Answer 37

**lead you to correct answer