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[h] SL 3.6 Pythagorean identities
[q] Pyhtagorean Identity
[a] Going back to the right-angled traingle in the unit circle again, one thing we can do here is to apply the Pythagorean Theorem, i.e: \(a^2+b^2=c^2\). In this case, \(sin^2\theta+cos^2\theta=1\).
[q] Double angle formula
[a] These are formulae for \(sin2\theta\) and \(cos2\theta\), both in terms of just \(sin\theta\) or \(cos\theta\). These can also be helpful for proving identities and solving trigonometric equations.
[q] \(sin2\theta\)
[a] \(sin2\theta = 2sin\theta×cos\theta\)
[q] \(cos2\theta\)
[a] \(cos2\theta = cos^2\theta-sin^2\theta = 2cos^2\theta-1=1-2sin^2\theta\)
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