Question

Find all solutions to the equation 2cosx - cscx = 0

Answer 1

\[2\cos(x) - \csc(x)=0\]
\[2\cos(x) - \frac{ 1 }{ \sin(x) }=0\]
\[\frac{ 2\sin(x)\cos(x)-1 }{ \sin(x) }=0\]
\[\frac{ \sin(2x)-1 }{ \sin(x) }=0\]
\[\sin(2x)-1=0\]
\[\sin(2x)=1\]
\[2x =\frac{ \pi }{ 2 },\frac{ 3\pi }{ 2 },\frac{ 5\pi }{ 2 },...\]
\[x=\frac{ \pi }{ 4 },\frac{ 3\pi }{ 4 },\frac{ 5\pi }{ 2 }\]

Answer 2

oops that very last item should be 5pi / 4

Answer 3

Another way of covering all possible values of x is to say
x = n*pi/4 where n can be any odd integer.

Answer 4

Thanks!