Question

18 sin178 * cos178 /sin356

Answer 1

18 sin178 * cos178 /sin356=(18sin178*cos178)/(2sin178*cos178)=18/2=9

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Answer 2

To simplify the expression 18 * sin(178°) * cos(178°) / sin(356°), you can use trigonometric identities to simplify it.

1. First, notice that sin(356°) is equal to -sin(4°) because sin is an odd function, meaning sin(-x) = -sin(x).

2. Then, use the sum-to-product identities for sin:

sin(A + B) = sin(A) * cos(B) + cos(A) * sin(B)

In this case, A = 178° and B = -4° (notice that I used the negative angle for B to match the signs of sin(356°)):

sin(178° - 4°) = sin(174°)

3. So, your expression can be simplified as follows:

18 * sin(178°) * cos(178°) / sin(356°) = 18 * sin(178°) * cos(178°) / sin(174°)

4. Now, use the double angle identity for sine:

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

In this case, A = 178°:

sin(356°) = 2 * sin(178°) * cos(178°)

5. Now, you can rewrite your expression using this result:

18 * sin(178°) * cos(178°) / (2 * sin(178°) * cos(178°))

6. Notice that sin(178°) * cos(178°) appears in both the numerator and denominator, so they cancel out:

18 / (2) = 9

So, the simplified value of the expression is 9.