I don't understand why #1 is "does not exist" as opposed to 0. I also don't know how to begin solving #2 and #3. When I look it up, the only solutions involve L'Hopital's Rule but my teacher hasn't taught us it yet so I can't use it. Any help is appreciated!
Answer
For the first one the expression under the radical sign is negative for θ≠π/2 so it is not real.
For the second one multiply top and bottom by 1−cosπx and turn the top into sin2πx
Then write the tan2πxof the bottom in terms of sinπx and cosπx and cancel the sin2πx from top and bottom.
The rest is easy.
The third one is similar to the second one.
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