Final answer:
To find the exact value of the trigonometric expression (sin 45°)(cos 45°)+(sin 30°)(cos 60°), we use the known sine and cosine values of these angles to get 1/2 + 1/4, which simplifies to 3/4.
Step-by-step explanation:
To determine the exact value of each trigonometric expression (sin 45°)(cos 45°)+(sin 30°)(cos 60°), we need to utilize the known values of sine and cosine for these specific angles, which are common in trigonometry.
For the first part, (sin 45°)(cos 45°), since sin 45° = cos 45° = √1/2, the product is (√1/2)(√1/2) = 1/2.
For the second part, (sin 30°)(cos 60°), sin 30° is 1/2 and cos 60° is also 1/2, hence, the product is (1/2)(1/2) = 1/4.
Adding both products together, we get 1/2 + 1/4 = 3/4. Therefore, the exact value of the trigonometric expression is 3/4.