How do you solve $sec x csc x = 2 csc x$ $secxcscx=2cscx$ ?

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Answer 1 · 2016-10-15T09:28:26

General solution is $x = 2 n π \pm \frac{π}{3}$ $x=2npi+-pi/3$ , where $n$ $n$ is an integer.

$sec x csc x = 2 csc x$ $secxcscx=2cscx$

Hence, considering $csc x \neq 0$ $cscx!=0$ , $sec x = 2$ $secx=2$

and so $x = \pm \frac{π}{3}$ $x=+-pi/3$ - note that $csc (\pm \frac{π}{3}) \neq 0$ $csc(+-pi/3)!=0$

and as all trigonometric functions are cyclic over $2 π$ $2pi$ ,

General solution is $x = 2 n π \pm \frac{π}{3}$ $x=2npi+-pi/3$ , where $n$ $n$ is an integer.

How do you solve secxcscx=2cscxsecxcscx=2cscxsecxcscx=2cscx?