Question

Алгебра 6sin15°*sin105°

Answer 1

6sin15°*sin105° = 3*2 sin15°*sin105° = 3( cos(-90°) - cos120°) =

3(-1 + (-1/2))=3*(-1,5)=-4,5

Answer 2

To calculate the expression 6sin15° * sin105°, we need to use trigonometric identities and formulas. Let's break it down step by step:

1. Convert the angles to their equivalent angles in the first quadrant: sin15° = sin(180° - 15°) = sin165° sin105° = sin(180° - 105°) = sin75°

2. Apply the product-to-sum formula: sin A * sin B = (1/2) * [cos(A - B) - cos(A + B)]

   For our expression, A = 165° and B = 75°: 6sin15° * sin105° = 6 * (1/2) * [cos(165° - 75°) - cos(165° + 75°)]

3. Simplify the angles in the cosine functions: cos(165° - 75°) = cos90° = 0 cos(165° + 75°) = cos240° = -1/2

4. Substitute the simplified values back into the expression: 6sin15° * sin105° = 6 * (1/2) * [0 - (-1/2)] = 6 * (1/2) * (1/2) = 3/2

Therefore, 6sin15° * sin105° simplifies to 3/2 or 1.5.