Answer:
Explanation:
To simplify the expression 3 sin² 60° * 4 tan² 30°, we need to apply the trigonometric identities for sine squared and tangent squared.
Step 1: Calculate sin² 60°:
The sine of 60 degrees is equal to √3/2. Therefore, sin² 60° = (√3/2)² = 3/4.
Step 2: Calculate tan² 30°:
The tangent of 30 degrees is equal to 1/√3. Therefore, tan² 30° = (1/√3)² = 1/3.
Step 3: Multiply the two results:
3 sin² 60° * 4 tan² 30° = (3/4) * (4/3) = 1.
Therefore, the expression 3 sin² 60° * 4 tan² 30° simplifies to 1.