Question

If sin alpha + sinbeeta = a and cosalpha + cosBeeta= b then
inter 1st​

Answer 1

Answer:

cos(α+β)=(b²-a²) /(b²+a²)

Step-by-step explanation:

a=(sin α+sin Ᏸ) and b=(cos α+ cos Ᏸ)

so we can write,

a²+b²=(sin α+sin Ᏸ)²+(cos α+ cos Ᏸ)²

1. a²+b²=(sin²α+2sin α sin Ᏸ+sin² Ᏸ)+(cos²α+ 2cos α cos Ᏸ+cos²Ᏸ)
2. 2+2 cos(α-Ᏸ)--------------(1)
3. we can also write,b²-a²=(cos α+ cos Ᏸ)²-(sin α+sin Ᏸ)²
4. b²-a²=(cos²α+ 2cos α cos Ᏸ+cos²Ᏸ)-(sin²α+2sin α sin Ᏸ+sin² Ᏸ)
5. b²-a²=(cos²α-sin² Ᏸ)+(cos²Ᏸ-sin²α)-2 cos(α-Ᏸ)
6. b²-a²=2 cos(α+Ᏸ)cos(α-Ᏸ)+2 cos(α-Ᏸ)
7. b²-a²=cos(α+Ᏸ)(2+2cos(α-Ᏸ))-------2
8. from equation 1 and 2 we can write,b²-a²=cos(α+Ᏸ)(a²+b²)
9. cos(α+β)=(b²-a²) /(b²+a²)