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andreev551 [17]
2 years ago
14

Rewrite with only sin x and cos x.

Mathematics
1 answer:
Annette [7]2 years ago
7 0

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

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6 0
2 years ago
Twice the sum of four and x is three less than x.
aliya0001 [1]

Answer:

-11

Step-by-step explanation

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2(4+x)=x-3

8+2x=x-3

Combining similar terms

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7 0
2 years ago
Express the following equation in slope-intercept form: 13x - 3y = 18 Select the best answer from the choices provided. A. y = 3
AveGali [126]

Answer:

The equation in the slope-intercept form is y =  \frac{13}{3}x + -6 ⇒ C

Step-by-step explanation:

The slope-intercept form of the linear equation is

y = m x + b, where

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  • b is the y-intercept

∵ The equation is 13x - 3y = 18

→ At first move x from the left side to the right side by subtracting 13x

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∴ 13x - 13x - 3y = 18 - 13x

∴ - 3y = 18 - 13x

→ Make the coefficient of y equal 1 by dividing both sides by -3

∵ \frac{-3y}{-3}=\frac{18}{-3}-\frac{13x}{-3}

∴ y = -6 - (-\frac{13}{3}x)

→ Remember (-)(-) = (+)

∴ y = -6 + \frac{13}{3}x

→ Switch the two terms of the right side

∴ y =  \frac{13}{3}x + - 6

∴ The equation in the slope-intercept form is y =  \frac{13}{3}x + -6

7 0
3 years ago
This table shows information about the number of
tatiyna

Answer:

Mean number of holidays taken =26.6

Step-by-step explanation:

To find the mean,

We use Σfx/Σf

Σfx =150+234+189+84+0+60

=717

Σf= 6+9+7+3+0+2

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Σfx/Σf= 717/27

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6 0
2 years ago
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Rudiy27

Answer:

78.5

Step-by-step explanation:

A=πr^2 is the formula. Since you're using pi as 3.14, 3.14 times 5^2 is 78.5 (5^2 is 25 because 5x5=25)

4 0
2 years ago
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