To solve this equation, we can use the cosine angle sum and difference identities:
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
Given that cos(70°+x)*cos(x-10°) = 1/2, we can rewrite the equation using the cosine angle sum and difference identities:
cos(70°)cos(x)cos(10°)sin(x) = 1/2
Since cos(70°) = cos(360° - 70°) = -cos(70°), and cos(10°) = cos(360° - 10°) = cos(10°), we can simplify the equation further:
-cos(70°)cos(x)cos(10°)sin(x) = 1/2
Applying the cosine angle identities, we get:
-[(cos(70°)cos(10°)sin(x))² - (cos(x)sin(70°)sin(10°))²] = 1/2
Solving for x requires trigonometric calculations that are beyond the capabilities of this text-based interface. I recommend using a graphing calculator or software to find the value of x that satisfies the equation.
To solve this equation, we can use the cosine angle sum and difference identities:
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
Given that cos(70°+x)*cos(x-10°) = 1/2, we can rewrite the equation using the cosine angle sum and difference identities:
cos(70°)cos(x)cos(10°)sin(x) = 1/2
Since cos(70°) = cos(360° - 70°) = -cos(70°), and cos(10°) = cos(360° - 10°) = cos(10°), we can simplify the equation further:
-cos(70°)cos(x)cos(10°)sin(x) = 1/2
Applying the cosine angle identities, we get:
-[(cos(70°)cos(10°)sin(x))² - (cos(x)sin(70°)sin(10°))²] = 1/2
Solving for x requires trigonometric calculations that are beyond the capabilities of this text-based interface. I recommend using a graphing calculator or software to find the value of x that satisfies the equation.