Question

Prove frac{sin(2x)}{sqrt{2-2cos(2x)}} = sin(x)

Answer 1

\[\frac{\sin(2x)}{\sqrt{2-2\cos(2x)}} = \sin(x) \]

Answer 2

u know the formula for cos 2x ?

Answer 3

and find any restrictions on x

Answer 4

i actually just need that part .. the restriction

Answer 5

ok, the denominator has square root sign and the expression under it cannot be negative.
Also , denominator cannot be 0.
make sense till here ?

Answer 6

yes

Answer 7

so\( 1-cos 2x \ne 0\)
so \(cos2x \ne 1\)
so 2x cannot equal 0,2pi,4pi,...
so x cannot equal 0,pi,2pi,3pi......
ok?

Answer 8

oh yeah .. cant remember properly but the test said the identity holds for 0<x<180 degrees.. is that true ?? idn if supposed to find that

Answer 9

seems correct, because cos 2x will be negative in 3rd quadrant, then denominator can no longer be 2cos x....so yeah.

Answer 10

how can i get that restriction ??

Answer 11

u need cos 2x to be negative, right ? only then u could write denominator as 2cos x
now, cos 2x negative implies, 2x is between 90 to 270 , right?
so actually here i am getting
x is between 45 to 135.... 45<x<135 as restriction....
does this makes sense?

Answer 12

yeah i get you

Answer 13

so overall restrictions are
45<x<135 and x \(\ne\) 0,180,360,......

Answer 14

can i solve 2-2cos(2x)>0
"?

Answer 15

if u solve that what u get?

Answer 16

x>0,pi,2pi,3pi

Answer 17

?

Answer 18

oh,nopes... when we take cos 2x as negative, we already took care of expression under square root to be positive....so need of that.

Answer 19

oh so you just solved 2-2cos(2x)=0 and 2-2cos(2x)<0

Answer 20

so is it 0<x<180 ??