AQA Core 4 4.06 Proving an identity using trig formulae

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sir how do you know which identity to use for the cos2x? is it because the denominator has sin so it would be easier? and if you didnt use that identity for the cos2x and used a different one like cos(squared)x-sin(squared)x then would you get the same answer?

khadijahammad
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I've proven identities by using both sides simultaneously before but my teacher has told me that I can't do that and I have to only use one side at a time. Please can you clarify if your sure that in the exam we can use both sides simultaneously or not. Btw I am doing AQA

husseinjusab
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The ones cancel but doesn't that leave '-2sin squared x'?

AdamSmith-pkxg
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Umm why does the equation sin squared 1/2x + cos squared 1/2x equals 1 but not 1/2 ... so if it does, doe stoat mean any number replacing 1/2 would always make the equation equal zero ... sorry a random question but it is tested on this topic exercise tha I'm doing

fstnukezz