Prove these identities: a) (sec x+cosec x)² tan x = (tan x + 1)² (tan x + cot x)

b)1+ tan²Alpha cosec²Beta/1+ tan²Alpha cosec² theta = 1+ sin²Alpha cot²Beta/1+ sin²Alpha cot²theta

c) 1+ 3 cos a - 4 cos³a/1- cos a = (1 + 2cosa)²

d) 1+ cosy - 2cos²y/sin²y = 1+ cosy/1+ cosy

e) 1- sin²A/1+ cosA + 1+ cosA/sinA - sinA/1- cosA = cot²A(1- cosA)