Evaluate the following: 2 tan2 45° + cos2 30° – sin2 60°

Sure, let's break it down:

1. Evaluate tan2 45°: The tangent of 45 degrees is 1. So, 2 * (tan2 45°) = 2 * 1 = 2.

2. Evaluate cos2 30°: The cosine of 30 degrees is √3/2. So, (cos2 30°) = (√3/2)^2 = 3/4.

3. Evaluate sin2 60°: The sine of 60 degrees is √3/2. So, (sin2 60°) = (√3/2)^2 = 3/4.

Now, substitute these values back into the original equation:

2 tan2 45° + cos2 30° – sin2 60° = 2 + 3/4 - 3/4 = 2.

So, 2 tan2 45° + cos2 30° – sin2 60° = 2.