Trigonometry Answers

If A+B+C=180 or if A+B+C=π, prove that asin(B-C)+bsin(C-A)+csin(A-B)=0.

Solve for x: tan[sup]2[/sup]x+cot[sup]2[/sup]x=2

Prove that:&
cos (θ-φ ) - sin (θ+φ/2) =-2 cos θ

& & The Statue of Liberty is 46 feet tall, and stands on a platform 47 feet tall. How far from the statue along the ground should I stand to get the largest viewing angle possible? (The "viewing angle" is the angle between the line connecting my eyes to the statue's feet, and the line connecting my eyes to the statue's crown.)

The length of a ramp is 150cm. Use trigonometry to show that when the angle, a (Located where the diagonal edge of the triangle meets the base), is 10 Degrees the height of the ramp, h, is 26.0cm, to one decimal place.

What steps would you take to verify this? Thank you!!! :)
(1-cos^2(x)) / ((1-sinx) (1+sinx)) = tan^2(x)

Re-write r=5sin(θ) in Cartesian coordinates.

How do I find the general sloution:

sin3x+sin2x=0.

A student stands a certain distance from a building and measures the angle to the top of the building as 18.8 degrees. The student then walks 24 ft straight towards the building and measures the angle to the top of the building as 20.2 degrees.
a) What is the height of the building, and
b) How close was the student to the bottom of the building after she had walked the 24 ft?

A ship travels 18.5 km on a course of 31.2 degrees south of east, then 12.7 km due south, then 21.5 km on the course of 61.3 degrees west of south, where it lands. Find the displacement and the angle traveled from the starting point to the landing point.