Question

Sin(2x) * cos (45градусов - x) = 0

Answer 1

task/29507989    Решить уравнение :  Sin(2x) * cos (45° - x) = 0 .                                    --------------------------

||cos (45°- x) =cos (x - π/4)_четная функция ||   Sin(2x) * cos (x -π/4 ) = 0 ⇔

[ Sin(2x) =0 ;  cos (x -π/4 ) = 0 .

a) sin2x =0 ⇔2x = πn ,n  ∈ℤ . ⇒ x =(π/2)*n ,n  ∈ℤ .

b) cos (x -π/4 ) = 0⇔x -π/4 = π/2+πn ,n  ∈ℤ . ⇒x = 3π/4+πn ,n  ∈ℤ .

Answer 2

To solve the equation Sin(2x) * cos(45 degrees - x) = 0, we need to find the values of x that satisfy the equation. When the product of two factors is equal to zero, one or both of the factors must be zero. Therefore, we can set each factor separately to zero and solve for x.

1. Sin(2x) = 0: The solutions to this equation can be found by setting 2x equal to integer multiples of π (pi), because the sine function is zero at these points.

   So, 2x = nπ, where n is an integer. => x = nπ/2, where n is an integer.

2. cos(45 degrees - x) = 0: The solutions to this equation can be found by setting (45 degrees - x) equal to odd multiples of π/2 (90 degrees), because the cosine function is zero at these points.

   So, 45 degrees - x = (2m + 1) * π/2, where m is an integer. => x = 45 degrees - (2m + 1) * π/2, where m is an integer.

Keep in mind that π radians is approximately equal to 3.14159, and 1 radian is approximately 57.2958 degrees.

Now we have two sets of solutions:

1. For Sin(2x) = 0: x = nπ/2, where n is an integer.

2. For cos(45 degrees - x) = 0: x = 45 degrees - (2m + 1) * π/2, where m is an integer.

Combine both sets of solutions to get all possible values of x that satisfy the original equation. Keep in mind that x can be in either degrees or radians, depending on the context of the problem.