SOLUTION: find all solutions of the equation in the interval [0,2pi): cos(x)+sin(x)tan(x)=2

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Question 106800This question is from textbook Precalculus with limits
: find all solutions of the equation in the interval [0,2pi):
cos(x)+sin(x)tan(x)=2 This question is from textbook Precalculus with limits

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
cos%28x%29%2Bsin%28x%29tan%28x%29=2 Start with the given equation


cos%28x%29%2Bsin%28x%29%28sin%28x%29%2Fcos%28x%29%29=2 Rewrite tan%28x%29 as sin%28x%29%2Fcos%28x%29



cos%28x%29%28cos%28x%29%2Bsin%28x%29%28sin%28x%29%2Fcos%28x%29%29%29=2%2Acos%28x%29 Multiply both sides by the LCD cos(x). This will eliminate the fraction



%28cos%28x%29%29%5E2%2B%28sin%28x%29%29%5E2=2%2Acos%28x%29 Distribute and multiply


1=2%2Acos%28x%29 Rewrite %28cos%28x%29%29%5E2%2B%28sin%28x%29%29%5E2 as 1


1%2F2=cos%28x%29 Divide both sides by 2


%28cos%281%2F2%29%29%5E-1=x Take the inverse cosine of both sides



pi%2F3%2B2pi%2An=x Take the inverse cosine of 1/2


So our answer is

x=pi%2F3%2B2pi%2An