The given equation, cos40° cosx + sin 40° sin x, can be simplified using the formula for the cosine of a difference of two angles: cos(A - B) = cosA cosB + sinA sinB.
This gives us that our equation is equivalent to cos(x - 40°) = √3/2.
Now we need to solve for x in this new equation.
The angles for which cosine is √3/2 are 30° and 330° (in the range from 0° to 360°). Therefore, we have:
x - 40° = 30°
=> x = 70°
and
x - 40° = 330°
=> x = 370°
However, since we want 0° ≤ x ≤ 360°, the solution x = 370° is not in the feasible range.
Therefore, the solution to the equation is x = 70°.
Solve the equation
Cos40° Cosx + sin 40° sin x=square root 3/2 for 0° less than or equal to x less than or equal to 360°
1 answer