Answer:
cos(2x) = 1 - 2sin²(x)
cos(2x) = 2cos²(x) - 1
1/cos(x) = sec(x)
1) (1-cos(2x))/cos(x) = 2sec(x)sin²(x)
Starting from LHS
(1- (1 - 2sin²(x))/cos(x)
2sin²(x)/cos(x)
2sec(x)sin²(x) = RHS
2) 1/sec²(x) = 1 + cos(2x) - cos²(x)
Starting form RHS
1 + 2cos²(x) - 1 - cos²x
cos²x
(1/sec(x))²
1/sec²(x) = LHS