Problem

Solve for x in the equation cos⁡(x)cos⁡(x)−sin⁡(x)=2

Answer

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Answer

Step 7: Solve for x: x=arctan⁡(12)

Steps

Step 1 ：Step 1: Rearrange the equation to have 0 on one side: cos⁡(x)cos⁡(x)−sin⁡(x)−2=0

Step 2 ：Step 2: Combine the two fractions on the left side of the equation: 2cos⁡(x)−2sin⁡(x)−cos⁡(x)cos⁡(x)−sin⁡(x)=0

Step 3 ：Step 3: Simplify the numerator: cos⁡(x)−2sin⁡(x)cos⁡(x)−sin⁡(x)=0

Step 4 ：Step 4: Use partial fraction decomposition to split the fraction: 1−2tan⁡(x)1−tan⁡(x)=0

Step 5 ：Step 5: Simplify the equation: 1−2tan⁡(x)=0

Step 6 ：Step 6: Solve for tan⁡(x): tan⁡(x)=12

Step 7 ：Step 7: Solve for x: x=arctan⁡(12)

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