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3 years ago

In the figure, line m is || line n. Name a pair of supplementary angles.

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

8 0

Angle 1 and angle 2
OR
Angle 3 and Angle 4

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Derive these identities using the addition or subtraction formulas for sine or cosine: sinacosb=(sin(a+b)+sin(a-b))/2

Sergeu [11.5K]

Answer:

The work is in the explanation.

Step-by-step explanation:

The sine addition identity is:

$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$ .

The sine difference identity is:

$\sin(a-b)=\sin(a)\cos(b)-\cos(a)\sin(a)$ .

The cosine addition identity is:

$\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$ .

The cosine difference identity is:

$\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)$ .

We need to find a way to put some or all of these together to get:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$ .

So I do notice on the right hand side the $\sin(a+b)$ and the $\sin(a-b)$ .

Let's start there then.

There is a plus sign in between them so let's add those together:

$\sin(a+b)+\sin(a-b)$

$=[\sin(a+b)]+[\sin(a-b)]$

$=[\sin(a)\cos(b)+\cos(a)\sin(b)]+[\sin(a)\cos(b)-\cos(a)\sin(b)]$

There are two pairs of like terms. I will gather them together so you can see it more clearly:

$=[\sin(a)\cos(b)+\sin(a)\cos(b)]+[\cos(a)\sin(b)-\cos(a)\sin(b)]$

$=2\sin(a)\cos(b)+0$

$=2\sin(a)\cos(b)$

So this implies:

$\sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)$

Divide both sides by 2:

$\frac{\sin(a+b)+\sin(a-b)}{2}=\sin(a)\cos(b)$

By the symmetric property we can write:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$

3 0

3 years ago

For which value of Theta is csc (Theta) undefined?

pantera1 [17]

The answer will be start fraction pi over 2 end fraction

8 0

3 years ago

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What’s the correct answer for this question?

Paladinen [302]

The second option.

Basically, you can use SAS.

3 0

3 years ago

Can someone help with surface area. I'll give them brainlyest

inessss [21]

Answer:

To fine the surface area is to add all the area of the faces

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3 years ago

Which will be the digit in ONE’S place in multiplication 3x5x7x9

Harman [31]

Answer:

Step-by-step explanation:

3x5x7x9=945

9 is in the hundreds place

4 is in the tens

which means 5 must be in the ones

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3 years ago

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