Question

Help with this question (100 points)

Answer 1

`\\ \rm\Rrightarrow sin(x+y)=(1)/(2)sinx+(√(3))/(2)cosx`

`\\ \rm\Rrightarrow sinxcosy+cosxsiny=(1)/(2)sinx+(√(3))/(2)cosx`

• Cancel sin and cos

`\\ \rm\Rrightarrow cosy+siny=(1)/(2)+(√(3))/(2)`

`\\ \rm\Rrightarrow cos(\pi)/(3)+sin(\pi)/(3)=(1)/(2)+(√(3))/(2)`

• y=π/3

Option B

Answer 2

y =
`(\pi)/(3)`

Explanation:

using the addition formula for sine

sin(x + y) = sinxcosy + cosxsiny

then

sinxcosy + cosxsiny =
`(1)/(2)` sinx +
`(√(3) )/(2)` cosx

for the 2 sides to be equal , then

cosy =
`(1)/(2)` and siny =
`(√(3) )/(2)`

then

y =
`cos^(-1)` (
`(1)/(2)` ) =
`(\pi )/(3)`

and

y =
`sin^(-1)` (
`(√(3) )/(2)` ) =
`(\pi )/(3)`

thus y =
`(\pi )/(3)`