5. Extend your arms out to either side.
6. Lean forward, lifting one leg straight behind you.
7. Hold this pose, then return your leg to the ground and your arms to the sides.
8. Repeat with opposite leg.
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Are they grammatical? Don't we have to put 'the' before 'opposite'?
5. OK
6. OK
7. Hold this pose; then return your leg to the ground and your arms to the sides.
[The word "then" is not a coordinating conjunction (one of the FANBOYS). It's a subordinating conjunction, and therefore needs different punctuation.]
http://www.chompchomp.com/terms/coordinatingconjunction.htm
Read the entire webpage to understand both coordinating and subordinating conjunctions.
8. Yes, this will read better if you put "the" in front of "opposite."
7. The semicolon is used in a compound sentence when no conjunction is used. The comma is appropriate when the conjunction is used to connect the sentences in a compound sentence.
I think we're splitting hairs here. "Then" may be used to begin a sentence. The semicolon is not incorrect here, but the comma may also be considered correct. I think no one, in this instance, is mistaken or wrong.
The sentences you provided are grammatically correct as they are. However, you are correct in saying that adding "the" before "opposite" can also be appropriate.
Using "the" is more specific and emphasizes that you are referring to the opposite leg in a particular context. It would be particularly useful if there has been previous mention or indication of the leg or if there are multiple options to choose from.
So, here's how the sentences would look with "the" added:
5. Extend your arms out to either side.
6. Lean forward, lifting one leg straight behind you.
7. Hold this pose, then return your leg to the ground and your arms to the sides.
8. Repeat with the opposite leg.
Both versions are grammatically correct, but using "the" gives a bit more clarity and specificity in the context of the exercise routine.