Math Questions and Answers

Start Your Free Trial

Prove that: (cosx)^3*(sinx)^2=1/16*(2cosx-cos3x-cos5x)

Expert Answers info

beckden eNotes educator | Certified Educator

calendarEducator since 2011

write562 answers

starTop subjects are Math, Science, and Business

 

`cos2x = cos^2x - sin^2x `

`sin2x = 2sinxcosx`

 

`cos3x = cosxcos2x - sinxsin2x = cosx(cos^2x-sin^2x) - sinx(2sinxcosx) `

 

`cos3x = cos^3x - cosxsin^2x - 2sin^2xcosx = cos^3x - 3sin^2xcosx `

 

`cos3x = cos^3x - 3(1-cos^2x)cosx = cos^3x - 3cosx + 3cos^3x `

 

`cos3x = 4cos^3x - 3cosx `

 

`sin3x = sin2xcosx + cos2xsinx = 2cosxsinxcosx + (2cos^2x - 1)sinx `

 

`sin3x = 2cos^2xsinx +...

(The entire section contains 242 words.)

Unlock This Answer Now


check Approved by eNotes Editorial