# Thread: compound angle formula problems

1. ## compound angle formula problems

If anyone could help me with these it would be greatly appreciated, I really have no idea how to start.

If sinx/siny = 1/2, and cosx/cosy = 3 prove sin(x+y) = 7/3sinxcosx

and

If cosx + sinx = 2/3, find the value of sin 2x

2. Originally Posted by ringo
If anyone could help me with these it would be greatly appreciated, I really have no idea how to start.

If sinx/siny = 1/2, and cosx/cosy = 3 prove sin(x+y) = 7/3sinxcosx

and

If cosx + sinx = 2/3, find the value of sin 2x
$\displaystyle sin(x) = \frac{1}{2}sin(y) \: rightarrow \: 2sin(x) = sin(y)$

$\displaystyle cos(x) = 3cos(y)$

$\displaystyle sin(x+y) = sin(x)cos(y) + cos(x)sin(y)$

Sub in the values you have for the above

3. Originally Posted by ringo
If anyone could help me with these it would be greatly appreciated, I really have no idea how to start.

If sinx/siny = 1/2, and cosx/cosy = 3 prove sin(x+y) = 7/3sinxcosx

and

If cosx + sinx = 2/3, find the value of sin 2x
HI

for the second part ,

cos x + sin x =2/3

square both sides , cos ^2 x + sin^2 x +2sin x cos x = 4/9

2 sin x cos x = 4/9 -1