2sinz-cosz=0,4

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To solve the equation 2sinz - cosz = 4, we can rearrange the terms to get:

2sinz = cosz + 4

Now, we can use the trigonometric identity sin^2(z) + cos^2(z) = 1 to substitute for sin^2(z), as follows:

4sin^2(z) = (1 - sin^2(z)) + 4
4sin^2(z) = 1 + 4 - sin^2(z) - 4
4sin^2(z) = 5 - sin^2(z)
5sin^2(z) = 5
sin^2(z) = 1

Taking the square root of both sides, we get:

sin(z) = ±1

Therefore, the solutions for z are z = π/2 + 2kπ and z = 3π/2 + 2kπ, where k is an integer.