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

Textbook Question

Chapter 5, 5.3 - Problem 30 - Precalculus (3rd Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

Posted on

`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)`

We’ve answered 318,947 questions. We can answer yours, too.

Ask a question