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3 years ago

Verify the identity sin^2(x)cos^2(x)=1/8(1-cos(4x))

Mathematics

1 answer:

bixtya [17]3 years ago

5 0

cos^2(x) = 1/2 + (1/2)cos(2x)

sin^2(x) = 1 - cos^2(x) = 1/2 - (1/2)cos(2x)

sin^2(x)cos^2(x)

= [1/2 - (1/2)cos(2x)][1/2 + (1/2)cos(2x)]

(a - b)(a + b) = a^2 - b^2

= (1/2)^2 - (1/2)^2[cos^2(2x)]

= 1/4 - (1/4)cos^2(2x)

= (1/4)[1 - cos^2(2x)]

= (1/4)[sin^2(2x)]

= (1/4)[1/2 - (1/2)cos(4x)]

= (1/4)(1/2)[1 - cos(4x)]

= (1/8)[1 - cos(4x)]

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Step-by-step explanation:

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3 years ago

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Find three consecutive integers whose sum is equal to −354. Three consecutive integers in ascending form are __,__,__

mixer [17]

Answer: -119, -120, and -121

Step-by-step explanation: This problem states that the sum of three consecutive integers is -354 and it asks us to find the integers. Three consecutive integers can be represented as followed.

X ⇒ first integer

X + 1 ⇒ second integer

X + 2 ⇒ third integer

Since the sum of our three consecutive integers is -354, we can set up an equation to represent this.

X + X + 1 + X + 2 = -354

Now, we can simplify on the left side of the equation.

3x + 3 = -354

-3 -3 ← subtract 3 on both sides of the equation

3x = -357

÷3 ÷3 ← divide both sides by 3

X = -119

X ⇒ first integer = -119

X + 1 ⇒ second integer = -120

X + 2 ⇒ third integer = -121

Therefore, our three consecutive integers are -119, -120, and -121.

6 0

3 years ago

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A movie theater has n rows and m seats in each row. If each ticket costs $5.60, how much do all tickets to one movie cost?

docker41 [41]

Answer:

All Tickets to one movie cost $\$5.60 \times m\times n$

Step-by-step explanation:

Given:

Number of rows in theater = n

Number of seats in each row = m

Total number of seats in the theater = Number of rows in theater $\times$ Number of seats in each row= $m \times n$

Now given each ticket costs = $\$5.60$

So to find total of all tickets we need multiply each ticket cost by Total number of seats in the theater

Total tickets cost = each ticket cost $\times$ Total number of seats in the theater = $\$5.60 \times m \times n$

3 0

3 years ago

Who do you solve 36×14usingpartial products by using 2-digit by 2-digit help

topjm [15]

first you would do this

4x6=24

then,4x30=120

then,10x30=300

then 10x6=60 lastly you would add them up and get a sum of 504

6 0

3 years ago

1/2 x^3 = 125/2 x=-5?

vlada-n [284]

ANSWER:

125/2 =125/2

PROVED

STEP BY STEP EXPLANATION

PUTTING THE VALUE OF X, WE HAVE

1/2×5×5×5=125/2

1/2×125=125/2

125/2=125/2

HENCE ,L.H.S =R.H.S

PROVED.

HOPE THIS WILL HELP YOU

3 0

3 years ago