Proof by contradiction help? (Student's proof starts by squaring both sides of inequality)

apple2357

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Thoughts on this question please?

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My query is this:
Can you go to the second step of the student proof from the first step? Something doesn't look right in the squaring?
squaring the inequality is only valid when sin x - cos x > 0...which it is because the angle is obtuse. But can you just assume that without proof?
Especially when the proof of it is to do with the signs of sin x and cos x, which is what the whole contradiction hangs on anyway???
 
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