Trig. Help (1 Viewer)

[bossleymaths]

prove that cos3x = 4cos^3 x - 3cosx

when i prove it i keep getting 4cos^3 x - 2cosx.... i cant get the three, this is what i have done

cos (2x + x)
cos 2x.cosx-sin2x.sinx
(2cos^2 x)(cosx) - (2sinxcosx)(sinx)
2cos^3 x - 2sin^2 x.cosx
2cos^3 x - 2(1-cos^2 x)(cosx)
2cos^3 x - 2cosx + 2cos^3 x
4cos^3 x -2 cosx

 

[tommykins]

prove that cos3x = 4cos^3 x - 3cosx

when i prove it i keep getting 4cos^3 x - 2cosx.... i cant get the three, this is what i have done

cos (2x + x)
cos 2x.cosx-sin2x.sinx
(2cos^2 x)(cosx) - (2sinxcosx)(sinx)
2cos^3 x - 2sin^2 x.cosx
2cos^3 x - 2(1-cos^2 x)(cosx)
2cos^3 x - 2cosx + 2cos^3 x
4cos^3 x -2 cosx

cos2x.cosx = cosx(cos^2x-[1-cos^2x]) = cosx(cos^2x - 1 + cos^2x) = cosx(2cos^3x-1) which is where your missing cos is

 

[tacogym27101990]

how good is de moivres theorem when it comes to these questions

 

[QuLiT]

waste of time. it's like a 4-5 line question demoires would require like 10

 

[tommykins]

how good is de moivres theorem when it comes to the questions

fkn oafz!

 

[laa.musique]

LHS = cos (2x + x)
cos 2x.cosx-sin2x.sinx
(2cos^2 x - 1)(cosx) - (2sinxcosx)(sinx)
2cos^3x -cosx -2sin^2xcosx
cosx(2cos^2x - 1 -2sin^2x)
cosx (2cos^2x - 1 - 2(1-cos^2x)
cosx(2cos^2x - 1 -2 + 2cos^2x)
cosx (4cos^2x -3)
= 4cos^3x - 3cosx


phew that was effort. but i hope it makes sense