[⅝ sec² 60°-tan² 60°+cos² 45°] is equal to

Sure, let's solve this step by step:

1. First, we need to calculate the values of sec² 60°, tan² 60°, and cos² 45°.

2. The secant of an angle in a right triangle is the hypotenuse divided by the adjacent side. For a 60° angle, sec 60° = 2. Therefore, sec² 60° = 2² = 4.

3. The tangent of an angle in a right triangle is the opposite side divided by the adjacent side. For a 60° angle, tan 60° = √3. Therefore, tan² 60° = (√3)² = 3.

4. The cosine of a 45° angle in a right triangle is √2/2. Therefore, cos² 45° = (√2/2)² = 1/2.

5. Now, we substitute these values back into the original equation: [⅝ sec² 60° - tan² 60° + cos² 45°] = [⅝ * 4 - 3 + 1/2] = [2.5 - 3 + 0.5] = 0.

So, [⅝ sec² 60° - tan² 60° + cos² 45°] is equal to 0.