Finding sine and cosine formulas

[rum2563]

[SOLVED] Finding sine and cosine formulas

Homework Statement

If sinx/siny = 1/2 and cosx/cosy = 3 prove:

sin (x + y) = 7/3 sinx cosx

Homework Equations

sin (x + y) = sinx cosy = cosx siny

The Attempt at a Solution

Can someone please give me a hint so that I can start? Thanks.

 

[rock.freak667]

Well fine cosy in terms of cosx from the 2nd formula and find siny in terms of sinx from the 1st formula and sub into the LHS of the proof

 

[rum2563]

Ok, here it goes:

* sinx/siny = 1/2

siny = 2sinx

* cosx/cosy = 3

cosy = cosx/3sin(x + y) = sinx cosy + cosx siny
= cosx/3 + 3 X 2sinx
= cosx/3 + 6sinx
= 7/3 sinx cosxIs this possibly right?
Please help. Thanks

 

[rock.freak667]

well that is correct...but you should put in the sinx and cosx in the 2nd and 3rd lines...or else it may seem weird that you simply got back the sinx and cosx at the end

 

[rum2563]

Well, If I put back sinx and cosx, then how will I get rid of them in the end?

 

[rock.freak667]

sin(x + y) = sinx cosy + cosx siny
= (sinxcosx)/3 + 2sinxcosx
=\frac{7sinxcosx}{3}

 

[rum2563]

Thanks very much rock.freak667. I finally get this.