Question

Solve for x sin(x-20) = cos(x)

Answer 1

Answer:

$x=\frac{6480^{\circ \:}n+1980^{\circ \:}}{36}$

$x=\frac{36\pi n+11\pi }{36}$

Step-by-step explanation:

We can use the identity: $\cos \left(x\right)=\sin \left(90^{\circ \:}-x\right)$ to simplify this into:$\sin \left(x-20^{\circ \:}\right)=\sin \left(90^{\circ \:}-x\right)$

The identity sin(x) = sin(y)  -->  $x=y+2\pi n,\:x=\pi -y+2\pi n$, can be used to simplify this further:

$x-20^{\circ \:}=90^{\circ \:}-x+360^{\circ \:}n$    (Add 20 to both sides)

$x=-x+360^{\circ \:}n+110^{\circ \:}$    (Add x to both sides)

$2x=360^{\circ \:}n+110^{\circ \:}$    (Divide both sides by 2)

$\frac{2x}{2}=\frac{360^{\circ \:}n}{2}+\frac{110^{\circ \:}}{2}$    (Simplify)

$x=\frac{6480^{\circ \:}n+1980^{\circ \:}}{36}$    If required, we can convert this into radians:

$x=\frac{36\pi n+11\pi }{36}$