even more identities for practice, includes sums of angles and

even more identities for practice, includes sums of angles and double angles
1.
( 1+tanA ) / ( 1-tanA ) = (cotA +1) / (cotA -1)
2.
1 - ( cos2A ) /( 1+sinA ) = sinA
3.
secA/cscA + sinA/cosA = 2 tanA
4.
sec4A - sec2A = tan4A + tan2A
5.
(sinA+cosA)2 + (sinA -cosA)2 = 2
6.
tan2A cos2A + cot2A sin2A = 1
7.
cotA / (1 - tanA ) + tanA / (1 - cotA ) = 1 + tanA + cotA
8.
(M sinA + N cosA)2 + (M cosA -N sinA)2 =M2 + N2
9.
[sinA + sin(3A) ] / 2 sin(2A) = cosA
10.
sinA [ sinA + sin(3A) ] = cosA [ cosA - cos(3A) ]
11.
[ sin(4A) + sin(2A) ] / [ cos(4A) + cos(2A) ] = tan(3A)
12.
[ cosA + cosB ] / [ cosA - cosB ] = - cot [ (A + B)/2 ] cot[ (A-B)/2]
13.
[ sin(4A) + sin(8A) ] / [ sin(4A) - sin(8A) ] = - tan(6A) / tan(2A)
14.
1 + cos(2A) + cos(4A) + cos(6A) = 4 cosA cos(2A) cos(3A)
15.
sin(4A) = 8 cos3A sinA -4 cosA sinA
16
sin1/2A cosA - sin5/2A cosA = cos3A sin1/2A