Question

Solve this equation:

sin(x + (π / 4)) – sin(x – (π / 4) = 1

Answer 1

use sin(a+b)=sina*cosb+cosa*sinb
sin(a-b)=sina*cosb-cosa*sinb

Answer 2

can you show me?

Answer 3

sin(x+pi/4)=sinx*cos(pi/4)+cosx*sin(pi/4)
=sinx/sqrt(2)+cosx/sqrt(2)...............1
sin(x-pi/4)=sinx*cos(pi/4)-cosx*sin(pi/4)
=sinx/sqrt(2)-cosx/sqrt(2).................2
substract (1)-(2)
2cosx/sqrt(2)=1
cosx=1/sqrt(2)
x=pi/4
that's ur answer

Answer 4

oh ok I follow that. is that the only answer or would there be another one?

Answer 5

i think thats the one

Answer 6

@Hero just to verify. @sidsiddhartha explained this really well

Answer 7

how did you go from 2cosx / sqrt2 = 1 to cosx=1/sqrt2. what happened to the 2 in 2cosx

Answer 8

@sidsiddhartha

Answer 9

2/sqrt(2)=sqrt(2)

Answer 10

thanks man! hopefully that is the only answer

Answer 11

@Hero can you just recheck this? wolfram doesn't agree but i may have entered it wrong

Answer 12

@washcaps, at some point, you have to be able to think yourself in this regard. He showed you the steps. If you understood it, and checked the answer, then there either is a mistake or there isn't one. If there is a mistake, you should be competent enough (if you understand the material) to go and locate where the mistake is. If there is no mistake, then you should check how you're inputting the information into wolfram. One way to check to see if a mistake was made is by graphing the trigonometric expression. For that, I recommend http://www.desmos.com

Answer 13

If we do all of the work for you, then you won't have learned anything useful for the next set of problems you'll be tasked with.

Answer 14

RIght. The equation and work looked fine to me, but wolfram didn't agree, so I don't know what to do. I can't find an error based off of what I know

Answer 15

I'm just saying, if it were me, I would be asking myself

Did I make a mistake while verifying the result?
Is there an algebraic mistake in the written solution?
Does the graph of the expression accurately reflect the given solution?

Answer 16

based off of my knowledge there was no mistake, but you seem to know this material, so I was just asking you if there was a problem

Answer 17

I showed you as much as I'm willing to show you for today

Answer 18

can you not just tell me if the answer is right or wrong? If it's right (which I think it is) then great. If its wrong, then I need to figure out why

Answer 19

@Hero can you help now?

Answer 20

@RadEn

Answer 21

You've been waiting here for three hours?

Answer 22

I figure that maybe you would have figured it out by now. All you have to do is apply the rule.

Answer 23

Have you tried doing it on your own. Applying the formula takes only a little bit of effort. As I said before, no one wants to do your work for you.