Question

Help with this question (100 points)

Answer 1

Answer:

y = $\frac{\pi}{3}$

Step-by-step explanation:

using the addition formula for sine

sin(x + y) = sinxcosy + cosxsiny

then

sinxcosy + cosxsiny = $\frac{1}{2}$ sinx + $\frac{\sqrt{3} }{2}$ cosx

for the 2 sides to be equal , then

cosy = $\frac{1}{2}$ and siny = $\frac{\sqrt{3} }{2}$

then

y = $cos^{-1}$ ($\frac{1}{2}$ ) = $\frac{\pi }{3}$

and

y = $sin^{-1}$ ( $\frac{\sqrt{3} }{2}$ ) = $\frac{\pi }{3}$

thus y = $\frac{\pi }{3}$