Updated - Trig Idents Problem.

BWJohnson

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Sep 27, 2016
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I have a problem which I have to expand and need to remove any powers or product terms similar to this, I know that trig idents will be used.

10(4SinA+SinB)+2(4SinA+SinB)2+0.5(4SinA+SinB)3

I understand that the first step could be to expand all of the brackets:

10(4SinA+SinB)+2(4SinA+SinB)(4SinA+SinB)+0.5(4SinA +SinB)(4SinA+SinB)(4SinA+SinB)
10(4SinA+SinB)+2(16Sin2A+8SinASinB+Sin2B)+0.5(16Sin2A+8SinASinB+Sin2​B)(4SinA+SinB)
10(4SinA+SinB)+2(16Sin2A+8SinASinB+Sin2B)+0.5(64Sin3A+48SinA2SinB+12SinASin2B+Sin3B)

Then I will multiply all of the terms in the bracket by the outside figure

40SinA+10SinB+32Sin2A+16SinASinB+2Sin2B+32Sin3A+24SinA2SinB+6SinASin2B+0.5Sin3B -these expressions do not need any trig idents
40SinA+10SinB+32Sin2A+16SinASinB+2Sin2B+32Sin3A+24SinA2SinB+6SinASin2B+0.5Sin3B -these expressions need the Sin2A=1/2(1-cos2A)
40SinA+10SinB+32Sin2A+16SinASinB+2Sin2B+32Sin3A+24SinA2SinB+6SinASin2B+0.5Sin3B -these expressions need the Sin3A=3/4SinA+1/4Sin3A
40SinA+10SinB+32Sin2A+16SinASinB+2Sin2B+32Sin3A+24SinA2SinB+6SinASin2B+0.5Sin3B -this expression needs the Sin(A)Sin(B)=1/2(cos(A-B)-cos(A+B)
40SinA+10SinB+32Sin2A+16SinASinB+2Sin2B+32Sin3A+24SinA2SinB+6SinASin2B+0.5Sin3B -these are the 2 im struggling with a bit!!!!

I can see that there is a square and a Product, do i apply the suare rule and then the COSSIN Product Rule for example;

6SinASin2B
6((SinA)(1/2(1-cos2B)) Apply the rule
6((SinA)(1/2-1/2cos2B)) Multiply terms within the answer by 1/2
6(1/2SinA-1/2SinACosB) Expand the brackets
3SinA-3SinACosB Multiply in 6 and this term now has no trig ident
3SinA-3(1/2(cos(A-B)-cos(A+B)) Apply the SinACosB rule
3SinA-3/2(cos(A-B)-cos(A+B)) Multiply in 3
3SinA-3/2cosA+3/2cosB-3/2cosA-3/2cosB All terms are now complete however they also all cancel out when summed together giving 0. This is not right as far as im aware, I have used Mathcad which gives a different final answer.

What is the correct process for applying the laws to this type of expression.
 
I have a problem which I have to expand and need to remove any powers or product terms similar to this, I know that trig idents will be used.

10(4SinA+SinB)+2(4SinA+SinB)2+0.5(4SinA+SinB)3

I understand that the first step could be to expand all of the brackets:

10(4SinA+SinB)+2(4SinA+SinB)(4SinA+SinB)+0.5(4SinA +SinB)(4SinA+SinB)(4SinA+SinB)
10(4SinA+SinB)+2(16Sin2A+8SinASinB+Sin2B)+0.5(16Sin2A+8SinASinB+Sin2​B)(4SinA+SinB)
10(4SinA+SinB)+2(16Sin2A+8SinASinB+Sin2B)+0.5(64Sin3A+48SinA2SinB+12SinASin2B+Sin3B)

Then I will multiply all of the terms in the bracket by the outside figure

40SinA+10SinB+32Sin2A+16SinASinB+2Sin2B+32Sin3A+24SinA2SinB+6SinASin2B+0.5Sin3B -these expressions do not need any trig idents
40SinA+10SinB+32Sin2A+16SinASinB+2Sin2B+32Sin3A+24SinA2SinB+6SinASin2B+0.5Sin3B -these expressions need the Sin2A=1/2(1-cos2A)
40SinA+10SinB+32Sin2A+16SinASinB+2Sin2B+32Sin3A+24SinA2SinB+6SinASin2B+0.5Sin3B -these expressions need the Sin3A=3/4SinA+1/4Sin3A
40SinA+10SinB+32Sin2A+16SinASinB+2Sin2B+32Sin3A+24SinA2SinB+6SinASin2B+0.5Sin3B -this expression needs the Sin(A)Sin(B)=1/2(cos(A-B)-cos(A+B)
40SinA+10SinB+32Sin2A+16SinASinB+2Sin2B+32Sin3A+24SinA2SinB+6SinASin2B+0.5Sin3B -these are the 2 im struggling with a bit!!!!

I can see that there is a square and a Product, do i apply the suare rule and then the COSSIN Product Rule for example;

6SinASin2B
6((SinA)(1/2(1-cos2B)) Apply the rule
6((SinA)(1/2-1/2cos2B)) Multiply terms within the answer by 1/2
6(1/2SinA-1/2SinACosB) Expand the brackets
3SinA-3SinACosB Multiply in 6 and this term now has no trig ident
3SinA-3(1/2(cos(A-B)-cos(A+B)) Apply the SinACosB rule
3SinA-3/2(cos(A-B)-cos(A+B)) Multiply in 3
3SinA-3/2cosA+3/2cosB-3/2cosA-3/2cosB All terms are now complete however they also all cancel out when summed together giving 0. This is not right as far as im aware, I have used Mathcad which gives a different final answer.

What is the correct process for applying the laws to this type of expression.
How is this an "update" of your original posting? (here) It doesn't look as though you've incorporated anything you've been provided at the original thread...? :shock:
 
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