How to calculate sin5 / 12 π × cos5 / 12 π? Please give the detailed process, thank you

How to calculate sin5 / 12 π × cos5 / 12 π? Please give the detailed process, thank you

[Note: sin2x = 2sinxcosx. Sin (π - x) = SiNx] original formula = (1 / 2) × 2Sin (5 π / 12) cos (5 π / 12) = (1 / 2) sin (5 π / 6) = (1 / 2) sin [π - (π / 6)] = (1 / 2) sin (π / 6) = (1 / 2) × (1 / 2) = 1 / 4

Given that the coordinates of a point on the terminal edge of angle α are (sin5 π / 6, cos5 π / 6), we can find the values of sin α and cos α

Establish the origin coordinates,
First, according to the coordinates of a point on the terminal edge of angle α as (sin5 π / 6, cos5 π / 6), the distance between the origin and the coordinates is calculated as 1
that
Sin α = opposite / hypotenuse = (cos5 π / 6) / 1 = cos π / 6 = √ 3 / 2
Cos α = adjacent / hypotenuse = (sin5 π / 6) / 1 = sin π / 6 = 1 / 2

The evaluation of (cot20 ° - radical 3) (cos5 ° + sin5 °) (cos5 ° - sin5 °) should be carried out in detail

(cot20 ° - radical 3) (cos5 ° + sin5 °) (cos5 ° - sin5 °) = (cot20 ° - radical 3). (cos5 ° ^ 2-sin5 ° ^ 2) = (cot20 ° - radical 3). Cos10 ° = (cos20 '/ sin20' - radical 3). Cos10 ° = (cos20 '/ 2sin10' - radical 3). Cos10 ° = cos20 '/ 2sin10' - radical 3