Question

6sin40°sin50°/cos10°​

Answer 1

Ответ:

Объяснение:

6*sin40°*sin50°/cos10°=6*sin50°*sin40°/cos10°=

=6*(1/2)*((cos(50°-40°)-cos(50°+cos40°))/cos10°=

=3*(cos10°-cos90°)/cos10°=3*(cos10°-0)/cos10°=3*cos10°/cos10°=3.

Answer 2

To simplify the expression 6sin40°sin50°/cos10°, we can use trigonometric identities.

Step 1: Convert degrees to radians since trigonometric functions in most mathematical libraries (including Python's math module) expect input in radians.

40° = 40 * π / 180 ≈ 0.69813 radians 50° = 50 * π / 180 ≈ 0.87267 radians 10° = 10 * π / 180 ≈ 0.17453 radians

Step 2: Apply the trigonometric identities:

sin(a) * sin(b) = (1/2) * [cos(a - b) - cos(a + b)] cos(a) = cos(-a)

Step 3: Substitute the values and calculate:

6 * sin(40°) * sin(50°) / cos(10°) = 6 * (1/2) * [cos(40° - 50°) - cos(40° + 50°)] / cos(10°) = 6 * (1/2) * [cos(-10°) - cos(90°)] / cos(10°) (since cos(a) = cos(-a) and cos(90°) = 0) = 6 * (1/2) * [cos(10°) - 0] / cos(10°) = 6 * (1/2) * cos(10°) / cos(10°) = 6 * (1/2) = 3

So, the simplified value of the expression is 3.