9sin50 / sin25*sin65

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вопрос

We can simplify this expression by using the trigonometric identity:

sin(2A) = 2sin(A)cos(A)

Let's rewrite the expression using this identity:

9sin(50) / sin(25)sin(65) = 9sin(50) / 0.5(sin(25)cos(25))

Since sin(50) = sin(50) and sin(65) = sin(65), we have:

9sin(50) / 0.5(sin(25)cos(25)) = 9sin(50) / 0.5(sin(65)cos(65))

Now, we can simplify this further:

9sin(50) / 0.5(sin(65)cos(65)) = 9sin(50) / sin(2 * 65)

Using the identity sin(2A) = 2sin(A)cos(A), we get:

9sin(50) / sin(130) = 9sin(50) / 0.5sin(130)

Therefore, the simplified expression is:

18sin(50) / sin(130)