Write the left side of the given expression as N/D, where N = sinA - sin3A + sin5A - sin7A D = cosA - cos3A - cos5A + cos7A Therefore we want to show that N/D = cot2A.
We shall use these identities: sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2) cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)
A two story home might use translation to have both floors identical and most homes have windows of the same size and shape so they might also use translation. Sometimes buildings use reflection to make rooms opposite each other the same.
