Prove and apply the Pythagorean identities. sin2(𝐴) + cos2(𝐴) = 1 tan2(𝐴) + 1 = sec2(𝐴) cot2(𝐴) + 1 = cosec2(𝐴)

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Prove and apply the identities for products of sines and cosines expressed as sums and differences. sin(𝐴) sin(𝐵) = 1 2 (cos(𝐴 − 𝐵) − cos(𝐴 + 𝐵)) cos(𝐴) cos(𝐵) = 1 2 (cos(𝐴 − 𝐵) + cos(𝐴 + 𝐵)) sin(𝐴) cos(𝐵) = 1 2 (sin(𝐴 + 𝐵) + sin(𝐴 − 𝐵)) cos(𝐴) sin(𝐵) = 1 2 (sin(𝐴 + 𝐵) − sin(𝐴 − 𝐵))