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Multiplication And Addition Trigonometry: cos (x – 𝛼) sin (x + 𝛼)

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cos (x – 𝛼) sin (x + 𝛼) = …?

SOLUTION

cos (x – 𝛼) sin (x + 𝛼) = ½ sin (x – 𝛼 + (x + 𝛼)) – ½ sin (x – 𝛼 – (x + 𝛼))

cos (x – 𝛼) sin (x + 𝛼) = ½ sin (2x) – ½ sin ( – 2𝛼 )

cos (x – 𝛼) sin (x + 𝛼) = ½ sin 2x + ½ sin 2𝛼

cos (x – 𝛼) sin (x + 𝛼) = ½ (sin 2x + sin 2𝛼)

 

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