# `sec(x)csc(x) = 2csc(x)` Find all the solutions of the equation in the interval `0,2pi)`.

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Expert Answers

gsarora17 | Certified Educator

`sec(x)csc(x)=2csc(x)`

`sec(x)csc(x)-2csc(x)=0`

`csc(x)(sec(x)-2)=0`

`csc(x)=0 , sec(x)=2`

No solutions for x for csc(x) in the rangeĀ `0<=x<=2pi`

General solutions for sec(x)=2 are

`x=pi/3+2pin , (5pi)/3+2pin`

Solutions for sec(x)=2 in the range are

`x=pi/3 ,(5pi/3)`