Quandaries and Queries


Who is asking: Student
Level: Secondary

The question is as follows:

"Express sin3A in terms of sinA and cosA."

I can only get work it out so far and then I end up back where I began. Any thoughts or clues to a solution would be greatly appreciated.




Write 3A as 2A + A to get

sib3A = sin(2A + A)

and then use the multiple angle expression for the sine.

sin(2A + A) = sin(2A)cos(A) + cos(2A)sin(A)

Now write 2A as A + A

sin(3A) = sin(A + A)cos(A) + cos(A + A)sin(A)

Finally expand sin(A + A) and cos(A + A) using the multiple angle expressions for sine and cosine.



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