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kondaur [170]
2 years ago
8

Cos²(90° -X).tan(180°-X).cos(180°+X)/sin(180°-X)

Mathematics
1 answer:
Naya [18.7K]2 years ago
3 0

Recall some identities:

tan(x) = sin(x) / cos(x)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

sin(x - y) = sin(x) cos(y) - cos(x) sin(y)

This means we have

• cos²(90° - x) = [cos(90°) cos(x) + sin(90°) sin(x)]²

… = sin²(x)

• tan(180° - x) = sin(180° - x) / cos(180° - x)

… = [sin(180°) cos(x) - cos(180°) sin(x)] / [cos(180°) cos(x) + sin(180°) sin(x)]

… = sin(x) / (-cos(x))

… = -tan(x)

(and we also get sin(180° - x) = sin(x))

• cos(180° + x) = cos(180°) cos(x) - sin(180°) sin(x)

… = -cos(x)

So, the given expression reduces to

sin²(x) (-tan(x)) (-cos(x)) / sin(x) = sin²(x)

since tan(x) and cos(x)/sin(x) = 1/tan(x) will cancel.

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Answer:

Option B is correct.

Step-by-step explanation:

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We need to find distance between origin and other point (3,-4,5)

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Putting values in the distance formula we get:

d=\sqrt{(3-0)^2+(-4+0)^2+(5-0)^2}\\d=\sqrt{(3)^2+(-4)^2+(5)^2}\\d=\sqrt{9+16+25}\\d=\sqrt{50}\\d=7

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STEP-BY-STEP EXPLANATION:

We have that the equation in its slope-intercept form is the following:

\begin{gathered} y=mx+b \\ m\text{ is the slope and b is the y-intercept } \end{gathered}

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