ExamBro
ExamBro
AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(A+B+C+D=2 \pi\), then \(\sin A+\sin B+\sin C+\sin D=\)

  1. A \(4 \sin \left(\frac{\mathrm{~A}+\mathrm{B}}{4}\right) \sin \left(\frac{\mathrm{A}+\mathrm{C}}{4}\right) \sin \left(\frac{\mathrm{A}+\mathrm{D}}{4}\right)\)
  2. B \(4 \sin \left(\frac{\mathrm{~A}+\mathrm{B}}{2}\right) \cos \left(\frac{\mathrm{A}+\mathrm{C}}{4}\right) \cos \left(\frac{\mathrm{A}+\mathrm{D}}{4}\right)\)
  3. C \(4 \sin \left(\frac{\mathrm{~A}+\mathrm{B}}{2}\right) \sin \left(\frac{\mathrm{A}+\mathrm{C}}{2}\right) \sin \left(\frac{\mathrm{A}+\mathrm{D}}{2}\right)\)
  4. D \(4 \sin \left(\frac{\mathrm{~A}+\mathrm{B}}{2}\right) \sin \left(\frac{\mathrm{A}+\mathrm{C}}{4}\right) \sin \left(\frac{\mathrm{A}+\mathrm{D}}{4}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(4 \sin \left(\frac{\mathrm{~A}+\mathrm{B}}{2}\right) \sin \left(\frac{\mathrm{A}+\mathrm{C}}{2}\right) \sin \left(\frac{\mathrm{A}+\mathrm{D}}{2}\right)\)

Step-by-step Solution

Detailed explanation

\( (\sin A+\sin B)+(\sin C+\sin D) = 2 \sin\left(\frac{A+B}{2}\right) \cos\left(\frac{A-B}{2}\right) + 2 \sin\left(\frac{C+D}{2}\right) \cos\left(\frac{C-D}{2}\right) \)…