Question

50*sin84*cos84 / sin168

Answer 1

Решение
50*sin84*cos84 / sin168 = [25*(2 sin84*cos84)] / sin168 =
=   [25*( sin168)] / sin168 =  25

Answer 2

We can simplify the expression using trigonometric identities. Recall that sin(2θ) = 2sin(θ)cos(θ), so we have:

sin(168) = sin(180 - 12) = sin(12)

Now, let's substitute this into the original expression:

50*sin(84)cos(84)/sin(168) = 50sin(84)*cos(84)/sin(12)

Next, recall the identity sin(90-θ) = cos(θ), so we have:

sin(84)*cos(84) = (1/2)sin(168)

Substituting this back into the original expression, we get:

50sin(84)cos(84)/sin(168) = 50(1/2)sin(168)/sin(12) = 25cot(12)

Therefore, the simplified expression is 25*cot(12).