Question

If sin A + Sin B = m and Cos A + Cos B = n .
Prove that :- Sin (A+ B) = 2mn / m²+n²

Answer 1

Answer:use common sense

Explanation:

Answer 2

for easy method
take
A=B=45°
sin A+sin B= m
1÷√2+ 1÷√2=m
√2=m
cos A+cos B=n
1÷√2+ 1÷√2=n
√2=n
given
R.H.S
2mn÷[m²+n²]
=2×√2×√2÷[(√2)²+(√2)²]
=2×2÷2+2
=4÷4
= 1
L.H.S
=sin (A+B)
=sin (45°+45°)
=sin 90°
=1