4sin15°sin75° - 1 Обчисліть

Question

4sin15°sin75° - 1
Обчисліть

Answer 1

4Sin15°Sin75° - 1 = 4Sin15°Sin(90° - 15°) - 1= 4Sin15°Cos15° - 1 =
= 2Sin30° - 1 = 2 * 1/2 - 1 = 1 - 1 = 0

Answer 2

4sin15°sin75°-1=?
sin^2(15°)=(1-cos30°)/2=(1-√3/2)/2=(2-√3)/4
sin15°=√(2-√3)/2
sin^2(75°)=(1-cos150°)/2=(1-cos(180°-30°))/2=
(1+cos30°)/2=(2+√3)/4
sin75°=√(2+√3)/2
4sin15°sin75°-1=4√((2+√3)(2-√3))/4-1=
√(4-3)-1=1-1=0