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sesenic [268]
4 years ago
6

Prove this identity using the product-to-sum identity for sin... sin^2 x=(1-cos(2x))/(2)

Mathematics
1 answer:
Simora [160]4 years ago
4 0

Answer:

sin²x = (1 - cos2x)/2 ⇒ proved down

Step-by-step explanation:

∵ sin²x = (sinx)(sinx) ⇒ add and subtract (cosx)(cosx)

(sinx)(sinx) + (cosx)(cosx) - (cosx)(cosx)

∵ (cosx)(cosx) - (sinx)(sinx) = cos(x + x) = cos2x

∴ - cos2x + cos²x = -cos2x + (1 - sin²x)

∴ 1 - cos2x - sin²x = (1 - cos2x)/2 ⇒ equality of the two sides

∴ (1 - cos2x) - 1/2(1 - cos2x) = sin²x

∴ 1/2(1 - cos2x) = sin²x

∴ sin²x = (1 - cos2x)/2

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4 years ago
Read 2 more answers
Consider the line y=−4/3x+3. Find the equation of the line that is parallel to this line and passes through the point , −4 6. Fi
andriy [413]

Answer:

The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .

The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .

Step-by-step explanation:

Parallel means equal slopes. Hence, the slope of the line parallel to y=4/3x+3 is 4/3 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.  

y−y1=m(x−x1)  

y−6=4/3(x−4)  

y−6=4/3x−16/3  

y=4/3x−7/3  

The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .

Question #2:

Perpendicular means negative reciprocal slopes. Hence, the slope perpendicular to y=4/3x+3 is y=−3/4 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.  

y−y1=m(x−x1)  

y−6=−3/4(x-4)  

y−6=−3/4x+6  

y=−3/4x+10

The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .

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2 years ago
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3 years ago
When factorising a quadratic trinomial of the form ax^2 + bx + c, we need to find two numbers which ???? (see image for options)
kupik [55]

Answer: Choice E

multiply to give a*c and add to get b

===========================================

This is known as the AC factoring method based on how you multiply the first and last coefficients (a and c) and use that product to figure out which factors add to the middle coefficient.

---------

An example:

6x^2 + 35x + 50

We have a = 6, b = 35, c = 50

Multiply a and c and we get: a*c = 6*50 = 300

We need to find factors of 300 that pair up and add to 35

Through trial and error you should find,

15 * 20 = 300

15 + 20 = 35

The two numbers are therefore 15 and 20.

So we break 35x into 15x+20x and use the factor by grouping method

6x^2 + 35x + 50

6x^2 + 15x + 20x + 50

(6x^2 + 15x) + (20x + 50)

3x(2x + 5) + 10(2x + 5)

(3x + 10)(2x + 5)

We see that 6x^2 + 35x + 50 factors to (3x + 10)(2x + 5)

Use the FOIL method or the box method or distribution to help see that (3x + 10)(2x + 5) expands back to 6x^2 + 35x + 50.

3 0
3 years ago
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