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In Fig. coil 1 and coil 2 are wound on a...

In Fig. coil `1` and coil `2` are wound on a long cylindrical insulator. The ends `A'` and `B` are joined together and current `I` is passed. Self-inductance of the two coils are `L_(1)` and `L_(2)`, and their mutual inductance is `M`.
a. Show that this combination can be replaced by a single coil of equivalent inductange given by
`L_(eq) = L_(1) + L_(2) + 2M`.
b. How could the coils be reconnected by yieldings an equivalent inductance of `L_(eq) = L_(1) + L_(2) - 2M`.

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