Answer:
[tex]x=\frac{6480^{\circ \:}n+1980^{\circ \:}}{36}[/tex]
[tex]x=\frac{36\pi n+11\pi }{36}[/tex]
Step-by-step explanation:
We can use the identity: [tex]\cos \left(x\right)=\sin \left(90^{\circ \:}-x\right)[/tex] to simplify this into:[tex]\sin \left(x-20^{\circ \:}\right)=\sin \left(90^{\circ \:}-x\right)[/tex]
The identity sin(x) = sin(y) --> [tex]x=y+2\pi n,\:x=\pi -y+2\pi n[/tex], can be used to simplify this further:
[tex]x-20^{\circ \:}=90^{\circ \:}-x+360^{\circ \:}n[/tex] (Add 20 to both sides)
[tex]x=-x+360^{\circ \:}n+110^{\circ \:}[/tex] (Add x to both sides)
[tex]2x=360^{\circ \:}n+110^{\circ \:}[/tex] (Divide both sides by 2)
[tex]\frac{2x}{2}=\frac{360^{\circ \:}n}{2}+\frac{110^{\circ \:}}{2}[/tex] (Simplify)
[tex]x=\frac{6480^{\circ \:}n+1980^{\circ \:}}{36}[/tex] If required, we can convert this into radians:
[tex]x=\frac{36\pi n+11\pi }{36}[/tex]
