Question regarding a trig equation

[rxh140630]

Homework Statement

cos(nθ) = cos((n-1)θ)cos(θ) - sin((n-1)θ)sin(θ)

Relevant Equations

no equation given for this trig equation

See the attached image. Apostol gives cos(nθ) = cos((n-1)θ)cos(θ) - sin((n-1)θ)sin(θ), in the middle of the picture, but previous info given does not state how he got this equation.

To me it looks like he used the equation cos(x+y) = cosxcosy-sinxsiny

 

[rxh140630]

If a moderator could please remove the thread I guess it actually was just using a previous equation that was given. I was too tired and understand why this is the result now.

 

[SammyS]

Homework Statement:: cos(nθ) = cos((n-1)θ)cos(θ) - sin((n-1)θ)sin(θ)
Relevant Equations:: no equation given for this trig equation

See the attached image. Apostol gives cos(nθ) = cos((n-1)θ)cos(θ) - sin((n-1)θ)sin(θ), in the middle of the picture, but previous info given does not state how he got this equation.

To me it looks like he used the equation cos(x+y) = cosxcosy-sinxsiny

A moderator may come along and remove this thread, as you wish. However, this formula comes directly from applying angle addition identities for cos. I guess you suspected as much.

$\cos(n\theta) = \cos((n-1)\theta+\theta)$

$= \cos((n-1)\theta)\cos(\theta)-\sin((n-1)\theta)\sin(\theta)$