Expert: Paul Klarreich - 4/27/2009

Question
Hi, im having a bit of trouble with this trigonometry proof question:

Using the two identities:
     sin(x+y)=sinxcosy + cosxsiny
     cos(x+y)=cosxcosy - sinxsiny
prove the following two identites:
     sin2θ=2sinθcosθ
     cos2θ=cosēθ-sinēθ

Any help would be greatly appreciated!
thankyou.

Answer
Questioner:   rachel
Country:  Australia
Category:  Calculus
Private:  No
 
Subject:  Trigonometry Question
Question:  Hi, im having a bit of trouble with this trigonometry proof question:

Using the two identities:
    sin(x+y)=sinxcosy + cosxsiny
    cos(x+y)=cosxcosy - sinxsiny
prove the following two identites:
    sin2θ=2sinθcosθ
    cos2θ=cosēθ-sinēθ

Any help would be greatly appreciated!
thankyou.
.............................................
Hi, Rachel,

You probably need a visit to your optometrist.  All you need to do is take:

    sin(x+y)=sinxcosy + cosxsiny
    cos(x+y)=cosxcosy - sinxsiny

and set x = θ  and  set  y = θ.

Then your 'double-angle' identities just drop out.