`cos(x) + sin(x)tan(x) = 2` Find all the solutions of the equation in the interval `0,2pi)`.

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Chapter 5, 5.3 - Problem 36 - Precalculus (3rd Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`cos(x)+sin(x)tan(x)=2`

`cos(x)+sin(x)(sin(x)/cos(x))=2`

`(cos^2(x)+sin^2(x))/cos(x)=2`

`1/cos(x)=2`

`cos(x)=1/2`

General solutions for cos(x)=1/2 are,

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

Solutions for the range `0<=x<=2pi`  are,

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

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