Theorem: letm,n be positive integers. Then: a) \\int_{-\\pi}^{\\pi}cos(mx)cos(nx

Question

Theorem: letm,n be positive integers. Then: a) int_{-pi}^{pi}cos(mx)cos(nx)dx=int_{-pi}^{pi}sin(mx)sin(nx)dx= pi if (m=n), 0if( m ?n) b) int_{-pi}^{pi} sin(mx)cos(nx)dx=0 Fill in the details in the proof of the theorem above: PROOF: consider the following product-to-sum formulas: cos A cos B = 1/2 cos(A-B)+ 1/2 cos (A+B) sin A sin B = 1/2 cos(A-B)- 1/2 cos (A+B) sin A cos B = 1/2 cos(A-B)+ 1/2 cos (A+B) a) int_{-pi}^{pi}cos(nx)cos(nx)dx =? b) for m?n, int_{-pi}^{pi}cos(mx)cos(nx)dx =? c) int_{-pi}^{pi}sin(nx)sin(nx)dx=? d) for m?n, int_{-pi}^{pi}sin(mx)sin(nx)dx=? e) int_{-pi}^{pi} sin(mx)cos(nx)dx=?

Explanation / Answer

Please post the question clearly...

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.