1)
2) & factorise.
3) Factorise and proceed as 2).
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About last formula, it requires a geometric reasoning to prove it, or you can also use complex numbers.
Find all solutions of the given equation:
1.) 2 sin x + 1 = 0
2.) sin 2x - cos x = 0
3.) sin² x - sin x = 0
**Not looking for the entire answer, just how to start.
Prove that the given trig identity is true:
cos (a - b) = (cos a) (cos b) + (sin a) (sin b)
**I know that it's true because it states the formula in the book but I just don't know how to prove it, lol.
Could you explain a little further on...all of them?
For #1, -1/2 is what I got on my own, but I don't know how to put the answer in terms of (ex. from another problem: x= pi/3 + 2n(pi) for any int n).
As for #2 and #3, can you give me the first step to factorizing? I'm clueless on where to start.
And #4...I still have no clue.
First of all, we're gonna find a formula for
Consider the following sketch:
Construction:
- Consider a rectangle
- Extend We get point
- Join &
- Extend We get point
- Draw now join &
- Let &
Start by showing that
We have
Rearrange
Finally, write and you'll get the desired formula.
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Now, a proof with complex numbers.
Finally
And we happily get
As desired.
The best way is to use --- but that is unfair.
Here is another geometric proof that I remember from 10th grade.
1)Construct the circle .
2)Construct those red lines touching at .
3) is the bigger angle from the x-axis.
4) is the smaller angle from the [tex]x-axis.
5)Coordinates of is .
6)Coordinates of is
7)The distance from is .
8)The angle between the two red lines is .
9)The length of using law of cosines is .
10)Equality of #7 and #9 leads to ...