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Question: Recursive trignometric transformations

Question:Recursive trignometric transformations

Rouben Rostamian 8269 Maple
trigonometric trigonometric-identities double-angle
June 07 2017
1

It is evident that by repeated applications of the double-angle and product trigonometric identities, one may transform any monomial of the form sin(x)^p * cos(y)^q, where p and q are positive integers, to a linear combination of only first powers of sines and cosines.

Example 1:  The monomial  4*sin(x)*cos(y)^2 is equivalent to

 

Example 2: The monomial 16*sin(x)^2*cos(y)^3 is equivalent to             

How does one write a Maple procedure to do that transformation in the general case of sin(x)^p * cos(y)^q?

 
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