Solve the equation

Question

Cos 40° Cos x +sin 40° sin x for 0° less than or equal to x less than or equal to 360

Answer 1

The given equation is:

cos(40°)cos(x) + sin(40°)sin(x)

Using the identity cos(A-B) = cosAcosB + sinAsinB, we can rewrite the equation as:

cos(40°-x)

Now, we set this equation equal to zero:

cos(40°-x) = 0

To find x in the interval 0° ≤ x ≤ 360°, we need to find the values of x that make cos(40°-x) equal to zero.

From the unit circle, we know that cos(40°-x) = 0 when the angle (40°-x) is 90° or 270°.

Set 40° - x = 90°:

40° - x = 90°
-x = 90° - 40°
-x = 50°
x = -50°

This solution is not in the given interval, so we discard it.

Set 40° - x = 270°:

40° - x = 270°
-x = 270° - 40°
-x = 230°
x = -230°

Similarly, this solution is not in the given interval, so we discard it.

Therefore, the given equation has no solution in the interval 0° ≤ x ≤ 360°.