Challenge your maths skills...
Question:
Express sin13θ in the form
Asinθ + Bsin^3θ + Csin^5θ +Dsin^7θ + Esin^9θ +Fsin11^θ + Gsin^13θ
A to G being natural numbers.
Have you ever seen summation notation before?
Basically it's a sum, and the limits on the sum are your counter.
So here, .
So k will go between 0 and .
The is a term in Pascal's triangle.
It might help if you did some research on summation (sigma) notation and Pascal's Triangle.
Summation - Wikipedia, the free encyclopedia
Pascal's triangle - Wikipedia, the free encyclopedia
First of all you should thank Prove It that he showed you the way rather than giving you the answer directly and that's the real spirit of MHF
Now it comes to your question , since you are still unable to catch with it , I will give you an example along with the step numbers**
example for
First step
Put n = 3 and accordingly k =1 so it becomes
Step 2
Expand the terms
--->
Remember that
So
Similarly
--->
Step 3
Now gather the values of each term
First term
Second term
Step 4
Add First and second term
Put this in the Step 2 which had those two terms
Thus we have expressed sin(3x) in terms of
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**Tell the step number you didn't get
-All you need to do is do the same way for sin(13x) find k, expand,find term values and go ahead