(sin 11П/18 - sin П/18)/(cos 11П/18 - cos П/18)

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вопрос

To simplify the expression, we can use the trigonometric identity:

sin(α) - sin(β) = 2sin((α-β)/2)cos((α+β)/2)

cos(α) - cos(β) = -2sin((α+β)/2)sin((α-β)/2)

So, the given expression becomes:

(2sin(5π/18)cos(6π/18)) / (-2sin(6π/18)sin(5π/18))
= (2sin(5π/18)cos(π/3)) / (-2sin(π/3)sin(5π/18))
= (2sin(5π/18) 1/2) / (-√3/2 sin(5π/18))
= -1/√3

Therefore, (sin (11π/18) - sin (π/18)) / (cos (11π/18) - cos (π/18)) simplifies to -1/√3.