Cos(2p-x)+sin(p/2+x)=корень из 2

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вопрос

To find the solution to the equation cos(2p-x) + sin(p/2+x) = √2, we can use trigonometric identities to simplify the equation.

First, remember the double angle identity for cosine: cos(2θ) = 2cos^2(θ) - 1. Applying this to the first term in the equation, we get:

cos(2p-x) = 2cos^2(p-x) - 1

Next, we can use the sum of angles formula for sine: sin(a + b) = sin(a)cos(b) + cos(a)sin(b). Applying this to the second term in the equation, we get:

sin(p/2 + x) = sin(p/2)cos(x) + cos(p/2)sin(x)
sin(p/2 + x) = cos(x) + sin(x)

Now our equation becomes:

2cos^2(p-x) - 1 + cos(x) + sin(x) = √2

Now we have a single equation with both cosine and sine terms. From here, we can utilize trigonometric identities such as Pythagorean identities and sum/difference of angles formulas to further simplify the equation and solve for the values of p and x.