Please help me with TRIG IDENTITIES? I've been working at these for hours.?

If you can show me how to solve any of these, that would be very helpful!


1) sinx + cosx = 1/tanx+cotx

2) sinx/cosx + secx/cscx = 2tanx

3) cotx-cot(2x) = csc2x (this may be csc^2x, the problem is handwritten so I can't tell for sure)

4) 2/(1+cos2x) = sec^2x

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