Question

If sine of the quantity x plus y end quantity equals radical 3 over 2 times sine of x plus one half times cosine of x comma what is the value of y?

pi over 2
pi over 3
pi over 4
pi over 6

Answer 1

Answer:

Step-by-step explanation:

$\text{sin}(x+y)=\dfrac{\sqrt3}{2}\text{sin}x+\dfrac{1}{2}\text{cos}x\\\\\text{or, sin}(x+y)=\text{sin}x\text{ cos}\dfrac{\pi}{6}+\text{sin}\dfrac{\pi}{6}\text{ cos}x\\\\\text{or, sin}(x+y)=\text{sin}\bigg(x+\dfrac{\pi}{6}\bigg)$

$\text{or, }x+y=x+\dfrac{\pi}{6}\\\text{or, }y=\dfrac{\pi}{6}$