trigonometry

can someone please explain why the worked solution (on the right) sets the function equal to sin2x?

How would I solve part a and b.

Any ideas? Solve cos^2theta - 5cos theta * sin theta + 6sin^2theta =0 between -pi ≤ theta ≤ pi

1. From a point P, a person observes that the angle of elevation of the top of a cliff A is 40°. After walking 100 m towards A along a straight road inclined upwards at an angle of 15° to the horizontal, the angle of elevation of A is observed to be 50°. Find the vertical height of A above P...

Hi Guys, In the screenshot I've attached (from my textbook), how is that 100 degree angle as well as that -40, 320 degree angle possible? I would have thought they would be around 350 and 100 respectively? Sorry if I'm missing something really obvious