Does double tap to wake consumes a lot of power on L720?

We don't know for sure.
On my 920 though, I have not noticed a difference. If you turn it on and still are happy with the battery life, go for it. I believe what little power cost is well worth it.
 
I tested this out on my Lumia 521. Usually, when its off, I come back from school with 90%. With it on, it was at 80%, so it was a big difference for me
 
Double tap to wake surely drains more battery, If someone is having battery issues, switch it off & use the power key instead
 
I use Double Tap. It's very convenient. I don't notice any difference in battery life. I'm happy with it.
 

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