Is the following statement true or false: If asked to solve for x in the following equation: `(1+sinx)/(cosx) + (cosx)/(1+sinx) = 4` For `0<=x<=2Pi` `x = Pi/2` ?

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embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

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Solve `(1+sinx)/(cosx)+(cosx)/(1+sinx)=4` :






If you divide both sides by 1+sinx you get:

`4cosx=2 ==> cosx=1/2 ==> x=pi/3,(5pi)/3` for `0<=x<=2pi`

However, these may not be the only solutions. If 1+sinx=0 then this equation holds. (Dividing by zero is not allowed, so this might represent a lost root.)

1+sinx=0 ==> sinx=-1 ==> `x=(3pi)/2`

But this solution does not work in the original equation as `cos((3pi)/2)=0` and you cannot divide by 0.


The solutions are `x=pi/3,(5pi)/3`


The graph:

Note that your solution is also impossible as `cos(pi/2)=0` and you would be dividing by zero in the first term.

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aruv | High School Teacher | (Level 2) Valedictorian

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``So your answer is not correct or falseĀ