How do I express the given sum or difference as a product of sines​ and/or cosines?

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1 Answer
Mar 19, 2018

#sin 3theta - sin theta = color(brown)( 2 cos (2theta) * sin theta = 2 sin theta - 4 sin^3 theta##

Explanation:

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From the above table, #sin a - sin b = 2 cos(a+b)/2 * sin (a-b)/2#

Given : #a = 3theta, b = theta#

Substituting for a & b in the above identity,

#sin 3theta - sin theta = 2 cos ((3theta + theta)/2) * sin ((3theta - theta)/2)#

#=>color(brown)( 2 cos (2theta) * sin theta = 2 sin theta - 2 sin^3 theta#