Question

Solve the following equations.
$sinxcos\frac{\pi }{8}+cosxsin\frac{\pi }{8}=\frac{1}{2},xϵ[-\frac{3\pi }{2},\pi ].$

Answer 1

$sinxcos\pi /8+cosxsin\pi /8=1/2$

$sin(x+\pi /8)=1/2$ $|xϵ[-3\pi /2,x]$

$x+\pi /8=4\pi +\pi /6(-1{)}^n$

$n=-2$ $x+\pi /8=-2\pi +\pi /6$

$h=-1$ $x=-\pi -\pi /6-\pi /8\Rightarrow x=\frac{31\pi }{24}$

$n=0$ $x=-\pi /8$

$n=1$ $x=\pi +\pi /6-\pi /8$