Question

Lf sinα+sinβ=a and cosα+cosβ=b, then write the value of sin(α+β)

Answer 1

sin+sin=2sin(+2)cos(−2)=sinα+sinβ=2
sin (
α
+

2
)
cos
⁡
(
α
−
β
2
)
=
a
(1)

cos+cos=2cos(+2)cos(−2)=
cos
⁡
α
+
cos
⁡
β
=
2
cos
⁡
(
α
+
β
2
)
cos
⁡
(
α
−
β
2
)
=
b
(2)

Divide (1) and (2) We get
tan(+2)=
tan
⁡
(
α
+
β
2
)
=
a
b
We have the formula

sin(+)=2tan(+2)1+tan2(+2)
sin
⁡
(
α
+
β
)
=
2
tan
⁡
(
α
+
β
2
)
1
+
tan
2
⁡
(
α
+
β
2
)
therefore
sin(+)=21+22=22+2