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+Sin2B)(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.
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+Sin2B)(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.