Prove that: (i) sinα+sinβ+sinγ−sin(α+β+γ)=4sin(α+β2)sin(β+�

1.	Prove that: (i) sinα+sinβ+sinγ−sin(α+β+γ)=4sin(α+β2)sin(β+γ2)sin(γ+α2) (ii) cos(A+B+C)+cos(A−B+C)+cos(A+B−C)+cos(−A+B+C)=4cosA cosB cosC
Answer» Prove that: (i) $s i n α + s i n β + s i n γ - s i n (α + β + γ) = 4 s i n (\frac{α + β}{2}) s i n (\frac{β + γ}{2}) s i n (\frac{γ + α}{2})$ (ii) $c o s (A + B + C) + c o s (A - B + C) + c o s (A + B - C) + c o s (- A + B + C) = 4 c o s A c o s B c o s C$

Prove that: (i) sinα+sinβ+sinγ−sin(α+β+γ)=4sin(α+β2)sin(β+γ2)sin(γ+α2) (ii) cos(A+B+C)+cos(A−B+C)+cos(A+B−C)+cos(−A+B+C)=4cosA cosB cosC

Answer»

Prove that:
(i) $s i n α + s i n β + s i n γ - s i n (α + β + γ) = 4 s i n (\frac{α + β}{2}) s i n (\frac{β + γ}{2}) s i n (\frac{γ + α}{2})$

(ii) $c o s (A + B + C) + c o s (A - B + C) + c o s (A + B - C) + c o s (- A + B + C) = 4 c o s A c o s B c o s C$