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Popular >

cos(x)+|cos(x)|=1,-2pi<= x<= 2pi

Solution

cos (x) + ∣ cos (x) ∣ = 1, - 2 π \leq x \leq 2 π

Solution

x = \frac{π}{3}, x = \frac{5 π}{3}, x = - \frac{5 π}{3}, x = - \frac{π}{3}

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Solution steps

cos (x) + ∣ cos (x) ∣ = 1, - 2 π \leq x \leq 2 π

Solve by substitution

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2}, - 2 π \leq x \leq 2 π : x = \frac{π}{3}, x = \frac{5 π}{3}, x = - \frac{5 π}{3}, x = - \frac{π}{3}

Combine all the solutions

x = \frac{π}{3}, x = \frac{5 π}{3}, x = - \frac{5 π}{3}, x = - \frac{π}{3}

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Frequently Asked Questions (FAQ)

What is the general solution for cos(x)+|cos(x)|=1,-2pi<= x<= 2pi ?
The general solution for cos(x)+|cos(x)|=1,-2pi<= x<= 2pi is x= pi/3 ,x=(5pi)/3 ,x=-(5pi)/3 ,x=-pi/3