2 соs( П/4-3х)= корень из 2

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To solve this equation, we need to isolate the variable x. Here's how to do it step by step:

Start by distributing the cosine function: 2 cos(π/4 - 3x) = √2

Divide both sides by 2: cos(π/4 - 3x) = √2 / 2

Take the inverse cosine of both sides to isolate x: π/4 - 3x = cos^(-1)(√2 / 2)

Substitute the value of cos^(-1)(√2 / 2) into the equation: π/4 - 3x = π/4

Now, solve for x: -3x = 0

Divide by -3 to isolate x: x = 0

Therefore, the solution to the equation 2 cos(π/4 - 3x) = √2 is x = 0.