Question

how do you sımplıfy sq.rt.1-4sın(x)^2?

Answer 1

I think you can do something like this. first, I let sqr aside, I will be back to it later. I have 1-4sin^2(x) = 1-2(1-cos(2x) =2cos(2x)-1 .Are you with me then?

Answer 2

yup

Answer 3

and cos2x = 2cos^2(x)+1 replace to 2cos (2x) and, now is your turn, do it.

Answer 4

I am not sure I understand what you are askıng me to substıtute where?

Answer 5

4cos^2(x)?

Answer 6

ok, wait few minutes. I don't do it yet., just give out my idea. but if you stuck, let me try. 50% believe on my stuff only, please.

Answer 7

where I am I supposed to substıtute what?

Answer 8

@niksva take it over. don't just send me something in secret. contribute, please

Answer 9

I don't know why, but I got a negative value of square root. It cannot be, right?

Answer 10

@jtthoma4 and @Hoa can we replace cos2x = cos^2(x) - sin^2(x) and 1 = sin^2(x) + cos^2(X) in the second step ? hope it will simplify the prob

Answer 11

@niksva I try, but it goes around and cannot be simplified still.

Answer 12

did you guys check the domain of the function?
\[1-4\sin^2(x)\ge0\]

Answer 13

ıs thıs a valıd statement; 2sq.rt.1-sın(x)^2

Answer 14

are you doing some sort of integration or differentiation?
and you want to make this a simple one?

Answer 15

@hoa after replacing i m getting \[\sqrt{\cos ^2(x)- 3\sin ^2(x)}\]

Answer 16

yeah, me too and I break 3sin^2 = sin^2 +2 sin^2 . and then cos^2 -sin^2 =1. I got 1-2sin^2 . you do next,

Answer 17

sorry, I am wrong at that stuff, cos^2 -sin^2 = cos 2x

Answer 18

and 2sin^2(x) = 1-cos 2x . . continue please

Answer 19

why do you bother? the person who asked the question does not even care!

Answer 20

@electrokid well said