Question

How can i verify this?

4 csc 2x = 2 csc^2x tan x

Answer 1

@mathmale hey math male do you have time to help?

Answer 2

(Limited time available right now. But hello!)

Suggestion: write 4 csc 2x as\[4\frac{ 1 }{ \sin 2x }\] and then use the appropriate identity for sin 2x. I'll be back on OpenStudy later this evening and may be able to help you continue with this then.

Answer 3

okay thanks!! ill work with this for now

Answer 4

do i use the double angle formula? for sin2x

Answer 5

It appears so.

Answer 6

so… it would look like this? \[1 \over 2 sinx cosx\]

Answer 7

@Luigi0210

Answer 8

\[\frac{4}{2\sin x \cos x}=\frac{2}{\sin x \cos x}\]
\[\frac{2}{\sin x \cos x} \times \frac{\sin x}{\sin x}=\]
\[\frac{2}{\sin ^2x}\times\frac{\sin x}{\cos x}=\]
\[2\csc ^2x \tan x\]

Answer 9

how did you do that, i don't understand half of this

Answer 10

how did you get the 4 to the numerator?

Answer 11

The 4 is in the numerator of the problem you posted.

Answer 12

\[4\csc 2x=\frac{4\csc 2x}{1}\]

Answer 13

See??? The 4 is part of the numerator.

Answer 14

yes, i see that.. I'm still a bit stumped on how you got from there to 4 over 2sinxcosx

Answer 15

\[\csc 2x=\frac{1}{\sin 2x}\]

Answer 16

\[\sin 2x=2\sin x \cos x\]

Answer 17

oh! alright i see now, I'm so bad at this i can never make the connections

Answer 18

how did you get cos onto the other side?

Answer 19

I didn't. I just reduced the fraction by cancelling the 2

Answer 20

how did cos go away lol… i still don't get it sorry

Answer 21

we can go from the right hand side, ok?
2 csc ^ 2 * tan = \(\dfrac{2}{sin^2}\) * \(\dfrac{sin}{cos}\) = \(\dfrac{2}{sin}*\dfrac{1}{cos}\)
now, time both numerator and denominator by 2, you have \(\dfrac{4}{2 sin cos}\)
and 2 sin cos = sin (2x), so that the fraction is \(\dfrac{4}{sin(2x)}= 4 csc(2x)\)

Answer 22

and how did you know to multiply by sin/sin

Answer 23

\[\frac{\sin x}{\cos x}=\tan x\]

Answer 24

I knew that I needed to get tan x. So I needed to have sin x in the numerator. The way to get it there was to multiply by sin/sin

Answer 25

is that a x tan or (times)tan @Loser66

Answer 26

your right hand side is \(\color{red}{2csc^2(x) tan (x)} \) right? I just don't type \((x)\), just the trigs

Answer 27

okay, yea i see it now, the right side seems easier! WOW i understand it now

Answer 28

@Loser66 THANK YOU!! explained it nice and simple

Answer 29

yw

Answer 30

i need help with another problem, could anyone help again?

Answer 31

Start from the right side: 2 csc^2 x *(tan x) =
= (2/sin^2 x)(sin x/cos x) = 2/(sin x*cos x) = 4/sin 2x
(because sin x*cos x = (sin 2x)/2).
Right side: 4/sec 2x = 4/sin 2x.
Finally, right side = left side

Answer 32

thank you!!