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3 years ago

Find the length of the missing leg.

Mathematics

1 answer:

Mariulka [41]3 years ago

5 0

ITS THE C OR 6 UR welcome

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Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

<em><u>Solution:</u></em>

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

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

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

$\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$

Applying this in above eqn 2, we get

$\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)$

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

7 0

3 years ago

I really need your help, but I don't get any.

STatiana [176]

Answer:

Step-by-step explanation:

x < -12, so x+12 < 0

| x-(-12) | = | x+12 | = -x-12

5 0

3 years ago

If gas prices are now $3.75 and they were up 10% from 6 months ago, how much were gas prices 6 months ago?

Hatshy [7]

Given

gas prices are now $3.75 and it up 10% from 6 months ago.

Find out how much were gas prices 6 months ago.

To proof

gas prices now = $3.75

let the gas price 6 month ago = x

gas price now is rise up 10% from 6 months ago

First write 10% in simpler form

$= \frac{10}{100}$

= 0.1

Now the equation becomes

0.1x + x = 3.75

1.1x = 3.75

$x =\frac{3.75}{1.1}$

x = 3.41 (approx)

Thus gas prices 6 months ago be $ 3.41 (approx )

Hence proved

7 0

3 years ago

Which one has a greater value, , -7 + (-7) or -7 - (-7)? Explain your answer. GIVING BRAINLIEST!!!

dmitriy555 [2]

-7 -(-7) because it will equal zero and the other one will be -14

6 0

3 years ago

20 point REWARD + Brainleist <3

jek_recluse [69]

B the answer is b because yiu do like add e square 27 +* 9 + x = 8 -/273/73

5 0

2 years ago

Read 2 more answers