Trigonometry

I saw on a website, law of sines are transposed. Example:
c^2=a^2+b^2-2abcos(C)
Transposed: cos(C)= a^2+b^2-c^2/2ab
I need a proof how it became this way.

express the function by a formula and draw the graph indicating that portion of the graph which has a meaning in the problem.

1. the amount of 1 dollar at 4% simple interest, as a function of time.

The equation says, sin2x=2sinxcosx
=2tanx/1+tan^2x
... How did they get 2tanx/1+tan^2x?

Proposition: The perimeter of a right triangle equals the altitude to the hypotenuse multiplied by the sum of the Tan's of 1/2 the acute∠’s, divided by the product of the Tan's of 1/2 the acute ∠’s

You may say this is a non-problem, and you would be right. Simply add up the lengths of all 3 sides.

However, the proposition seeks to reveal just one of many mysterious and profound ways of mathematics.

EXAMPLE:
To demonstrate, let the 8 15 17 Pythagorean triangle be our selection.

The angle of elevation of the tower from A is 25°. From another point B, the angle of elevation of the top of the tower is 56°. AB=300m and on the same horizontal plane as the foot of the tower. The horizontal angle subtended by A and B at the foot of the tower is 70°.

What is the height of the tower?
How far A from the tower?
How far B from the tower?

Problem: Find h,x,y,z,ϴ,Φ, and β.

Please help to solve this problem:
The angle of elevation of a point C from a point B is 29⁰42'; the angle of elevation of C from another point A 31.2 m directly below B is 59⁰23'. How high is C from the horizontal line through A?