cos3A

Cos3A

= cos(2A+A)

= cos2AcosA – sin2AsinA

= (2cos²A-1)cosA – 2sin²AcosA

= 2cos³A – cosA – 2(1-cos²A)cosA

= 2cos³A – cosA – 2cosA + 2cos³A

= 4cos³A – 3cosA

sin3A

ปรุฬห์ รุจนธำรงค์

sin3A

= sin(2A + A)

= sin2AcosA + cos2AsinA

=(2sinAcosA)cosA + (1-2sin²A)sinA

= 2sinAcos²A + (1-2sin²A)sinA

= 2sinA(1-sin²A) + sinA – 2sin³A

= 2sinA – 2sin³A + sinA – 2sin³A

= 3sinA – 4sin³A

ดังนั้น sin3A = 3sinA – 4sin³A