Solve for x (tan(x)-1)(cos(x)+1)=0

Problem

(tan(x)−1)*(cos(x)+1)=0

Solution

1. Apply the zero product property by setting each factor equal to zero.

tan(x)−1=0

cos(x)+1=0

2. Isolate the trigonometric functions in each equation.

tan(x)=1

cos(x)=−1

3. Solve for x in the first equation tan(x)=1 The tangent function is equal to 1 at π/4 and repeats every π radians.

x=π/4+n*π

4. Solve for x in the second equation cos(x)=−1 The cosine function is equal to −1 at π and repeats every 2*π radians.

x=π+2*n*π

5. Check for domain restrictions since tan(x) is undefined where cos(x)=0 The values found do not conflict with these restrictions.

6. Combine the solutions where n is any integer.

Final Answer

x=π/4+n*π,π+2*n*π

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