proving trig identities: 1 + sinx = (sin 1/2 x + cos 1/2 x)2

[Kanimoto]

Hi...these were some identities I was unable to prove. If anyone can help, thanks. The last number in the first problem is supposed represent the square of the term, and the 2 next to the tan in the last problem is also supposed to represent the square.

1. 1 + sin x = (sin 1/2 x + cos 1/2 x)2

2. tan 1/2 (A+B) = (sin A + sin B) divided by (cos A + cos B)

3. sin(x+y)cos y - cos(x+y)sin y = sin x

4. (1 + cos a + cos 2a) divided by (sin a + sin 2a) = ctn a

5. (2 sin x - sin 2x) divided by (2 sin x + sin 2x) = tan2 1/2 x

 

[royhaas]

This will get you started. Then show some work.

1. Use sin(x)=sin(x/2+x/2) along with 1=cos^2(x/2)+sin^2(x/2).
2. Start with the formula for the tangent of the sum of two angles.
3. Use x+y-y = x.