Question

ln|1+sinx|+ln|1-sinx|=2ln|cosx|

Answer 1

\(\large\color{black}{ \rm ln|~a~|~~+~~ln|~b~|~~=~~ln|~a\times b~|}\)

Answer 2

a = 1+sin(x)
b = 1-sin(x)

apply this rule:)

Answer 3

Need more clarification?

Answer 4

Ha! I got here!

Answer 5

okay, good:)
And how do you feel about my initial post?
Do you think you understand the rule, and can apply it to your problem?

Answer 6

I dont understand... can you FOIL 1-sinx ans 1+sinx?

Answer 7

yes, you can.

Answer 8

Yes.

Answer 9

Just like
(a-b)(a+b)=a^2-b^2

so will (1-sin x)( 1 + sin x) equal what?

Answer 10

2-sin2x?

Answer 11

why twos?

Answer 12

You meant \(1-\sin^2(x)\) yes?

Answer 13

*1... 1^2 is 1 :D

Answer 14

Good.

Answer 15

and the 2 inside the sin2x is supposed to be the power?

Answer 16

yes

Answer 17

Okay, now we have a rule.
(Pythagorean)

\(\large\color{black}{ \sin^2(x)+\cos^2(x)=1}\)

at first, can you tell me what will we get, IFF we subtract \(\large\color{black}{ \cos^2(x)}\) from both sides (of the rule).

Answer 18

1-sin2x=cos2x

Answer 19

yes.

Answer 20

and the you take the 2 to the outside?

Answer 21

so you already know that it will turn into cos^2x ! good!

Answer 22

Yes, the 2 goes on the outside as an exponenet.

Answer 23

(because cos^2x is same as (cos x)^2 )

Answer 24

Thank you so much! :)

Answer 25

Anytime... you are a very smart student!

Answer 26

Remember to medal the user who helped you the most. :)