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3 years ago

Find the slope plz help il give 33 points

Mathematics

1 answer:

Alik [6]3 years ago

5 0

You said you will give 33 points but it only says 17 points

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[tex]cos {}^{4} α+sin {}^{4} α= \frac{1}{4} (3+cos4α) Prove:

asambeis [7]

Given:

$\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)$

To prove:

The given statement.

Proof:

We have,

$\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)$

$LHS=\cos^4 \alpha+\sin^4\alpha$

$LHS=(\cos^2 \alpha)^2+(\sin^2 \alpha)^2$

$LHS=(\cos^2 \alpha+\sin^2\alpha)^2-2\sin ^2\alpha\cos^2 \alpha$ $[\because a^2+b^2=(a+b)^2-2ab]$

$LHS=(1)^2-2(1-\cos^2 \alpha)\cos^2 \alpha$ $[\because \cos^2 \alpha+\sin^2\alpha=1]$

$LHS=1-2\cos^2 \alpha+2\cos^4 \alpha$

Now,

$RHS=\dfrac{1}{4}(3+\cos 4 \alpha)$

$RHS=\dfrac{1}{4}[3+(2\cos^2 2\alpha-1)]$ $[\because \cos 2\theta=2\cos^2\theta -1]$

$RHS=\dfrac{1}{4}[2+2\cos^2 2\alpha]$

$RHS=\dfrac{1}{4}[2+2(2\cos^2 \alpha-1)^2]$ $[\because \cos 2\theta=2\cos^2\theta -1]$

$RHS=\dfrac{1}{4}[2+2(4\cos^4 \alpha-4\cos \alpha+1)]$ $[\because (a-b)^2=a^2-2ab+b^2]$

$RHS=\dfrac{1}{4}[2+8\cos^4 \alpha-8\cos \alpha+2]$

$RHS=\dfrac{1}{4}[4+8\cos^4 \alpha-8\cos \alpha]$

$RHS=1+2\cos^4 \alpha-2\cos \alpha$

$RHS=1-2\cos^2 \alpha+2\cos^4 \alpha$

$LHS=RHS$

Hence proved.

8 0

3 years ago

ABC is a straight line.

guapka [62]

Answer:

AB = 20 metres

BC = 60 metres

Step-by-step explanation:

Let AB = x

Then, BC = 3x

Condition:

=> x+3x = 80

=> 4x = 80

Dividing both sides by 4

=> x = 20

So,

AB = 20 metres

BC = 3(20)

BC = 60 metres

6 0

3 years ago

Read 2 more answers

Two cars start at the same point. One travels north at 65 km/h and the other travels east at 50 km/h. How far are they apart aft

Naya [18.7K]

Answer:

1they are 15 kilometers apart

7 0

3 years ago

Pls help me show all your workings

aleksley [76]

Answer:

1)I don't know

2)-2

Step-by-step explanation:

2)6-5(1/1/x)= 2

6-5(1/1)-x= 2

6-6-x=2

-x/-1=2/-1

x= -2

3 0

2 years ago

I need help because I don’t know diameter

Scorpion4ik [409]

Answer:

1. Divide

2. multiply

3. parenthesis

4. parenthesis

5. divide

Step-by-step explanation:

3 0

3 years ago