Integral using angle sum identity

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In this video, I showed how to modify and evaluate an integral using angle sum identities
  1. Prime Newtons
  2. AB/BC
  3. AP calculus
  4. Algebra
  5. Calc1
  6. Calc2
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Автор

I will use T for theta and give only the answer without the working as follows:
1/32 sin16T + 1/20 sin 10T + C.
I hope l am correct.
I must admit it's the first time I have seen an integration done like this.
Keep up the good work 👏.

EE-Spectrum
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... Good day Newton, For the homework integrand and T = Theta: Applying cosAcosB = (1/2)[cos(A + B) + cos(A - B)], where A =13T and B = 3T --> cos(13T)cos(3T) = (1/2)[cos(16T) + cos(10T)] --> (1/2)INT(cos(16T) + cos(10T))dT = (1/2)[(1/16)sin(16T) + (1/10)sin(10T)] + C = (1/32)sin(16T) + (1/20)sin(10T) + C ... I hope not having made mistakes Newton ... Thank you for the workout, Jan-W

jan-willemreens
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... sin(A + B) = sin(A)cos(B) + cos(A)sin(B) [ Remember that the sine function is odd: sin(- B) = - sin(B), and that the cos function is even: cos(- B) = cos(B) ] --> sin(A - B) = sin(A + (- B)) = sin(A)cos(- B) + cos(A)sin(- B) = sin(A)cos(B) - cos(A)sin(B) ... one can also apply these properties for the cosine formulas; thus SINE FUNCTION = ODD FUNCTION (SIN(- X) = - SIN(X)) and COSINE FUNCTION = EVEN FUNCTION (COS(- X) = COS(X)), never forget this, always very handy using Trigonometry! (lol) ... ( sin(A - B) = sin(A + (- B)) = .... etc. )

jan-willemreens