Solve for x arccos(x-1/( square root of 2))=pi/4

Problem

arccos(x−1/√(,2))=π/4

Solution

1. Apply the cosine function to both sides of the equation to isolate the expression inside the inverse cosine.

cos(arccos(x−1/√(,2)))=cos(π/4)

2. Simplify the left side using the property cos(arccos(θ))=θ and evaluate the right side using known trigonometric values.

x−1/√(,2)=√(,2)/2

3. Rewrite the fraction on the right side to have a common denominator or form with the term on the left, noting that √(,2)/2=1/√(,2)

x−1/√(,2)=1/√(,2)

4. Isolate x by adding 1/√(,2) to both sides of the equation.

x=1/√(,2)+1/√(,2)

5. Combine the terms to find the final value of x

x=2/√(,2)

6. Rationalize the denominator by multiplying the numerator and denominator by √(,2)

x=√(,2)

Final Answer

arccos(x−1/√(,2))=π/4⇒x=√(,2)

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