Prove \(\displaystyle{\sin{{\left(\alpha-\beta\right)}}}+{\sin{{\left(\alpha-\gamma\right)}}}+{\sin{{\left(\beta-\gamma\right)}}}={4}{\cos{{\frac{{\alpha-\beta}}{{{2}}}}}}{\sin{{\frac{{\alpha-\gamma}}{{{2}}}}}}{\cos{{\frac{{\beta-\gamma}}{{{2}}}}}}\)

Nadia Clayton

Nadia Clayton

Answered question


Prove sin(αβ)+sin(αγ)+sin(βγ)=4cosαβ2sinαγ2cosβγ2

Answer & Explanation

Lana Hamilton

Lana Hamilton

Beginner2022-03-31Added 12 answers

Finish off by using the formula for the cosine of a sum/difference, then set x=αβ and y=βγ

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