Identities of Expression

The attachment has 6 problems. Number 1 & 6 are a little hard to see on the attachment so see below of each. The zero's represents the phase angle symbol in the eqaution. I am trying to understand the method of deriving an expression for each and for number 6 is finding the least positive angle. Please rember there are only 6 problems, however on the attachment 1 & 6 maybe hard to read. 1.) 2 tan ( 0 / 2 ) = 6.) tan ( 45 + 0) -3 tan 0 = 2

Identity Expression

The following attachment has 7 each problems that I need help solving. From 1 to 5 are expression identities, 6 for solving and 7 has to be factor. Please see attached.

Expression

There are 3 problems. The first and second problem are with the dotted lines both are division problems. I am looking for the expression for each. 1) Sin(x + B) + cos( x - B) --------------------------- = Cos(x + B) - sin(x - B) 2.) Tan2x + sin2x = ----------------- Tan2x 3.) Cos^2( x + B) - cos^2 ( x - B) =

polar coordinates

x and y represents rectangular coordinates. What is the given equation using polar coordinates (r, theta). x^2 = 4y

dot product

If v = i - j and w = i + j, find the dot product v * w and the cosine of the angle between v and w.