Question

Help with maths to solve the task

Answer 1

A = 2cos(90°-α)•sin(90°+α)•tg(180°-α)/ctg(90°+α)•sin(180°-α).

α = 30°

A = 2cos(90°-30°)•sin(90°+30°)•tg(180°-30°)/ctg(90°+30°)•sin(180°-30°).


cos(90°-30°) = cos90°•cos30°+sin90°•sin30°
= 0•√3/2+1•1/2 = 1/2.

sin(90°+30°) = sin90°•cos30°+sin30°•cos90°
= 1•√3/2+1/2•0 = √3/2.

tg(180°-30°) = tg180°-tg30°/1+tg180°•tg30°
= 0-√3/3/1+0•√3/3 = -√3/3.

ctg(90°+30°) = ctg90°•ctg30°+1/ctg30°-ctg90°
= 0•√3+1/√3-0 = 1/√3 = √3/3.

sin(180°-30°) = sin180°•cos30°-sin30°•cos180°
= 0•√3/2-1/2•(-1) = 1/2.




A = 2•1/2•√3/2•(-√3/3)/√3/3•1/2
A = -3/6/√3/6
A = -3/6•6/√3
A = -3/√3
A = -√3.




Little White Lies