Help with trig proof and limit question?? (1 Viewer)

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Hey there,

I'm having some troubles with this question here. I think I know what to do to prove the two equations but I'm not really sure if I'm doing the limit part right . Could someone give me a hand? Thanks in advance! (Question attached).
 

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fan96

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Note that before we do anything else, must be nonzero.

Also, to apply the identity we require

One method is



and using the standard result



leads to the answer.

(This method doesn't work for but this case is trivial to verify separately.)
 
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