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sesenic [268]
3 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]3 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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Answer:

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Step-by-step explanation:

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2 years ago
Find the equation of the line passing through the points (3,-2) and (4,6) in slope intercept form.​
noname [10]

Hey!

------------------------------------------------

They already give us the slope, so we can solve the y-intercept.

We can use (3, -2).

y = 8x + b

-2 = 8(3) + b

-2 = 24 + b

-2 - 24 = 24 + b - 24

-26 = b

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Hence, the answer is \Large\boxed{\mathsf{y~=~8x~+~-26}}

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Hope This Helped! Good Luck!

4 0
3 years ago
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Ivenika [448]
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4 0
3 years ago
The graph of y = StartAbsoluteValue x EndAbsoluteValue is transformed as shown in the graph below. Which equation represents the
iogann1982 [59]

Using translation concepts, it is found that the equation of the transformed function is:

y = |x + 3| - 2.

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The absolute value function is given by y = |x|, and has vertex at (0,0). After the transformations, the function has vertex (-3, -2), which means that:

  • It was shifted 3 units to the left, hence x -> x + 3.
  • It was shifted 2 units down, hence y -> y - 2.

Thus, the equation of the function is now given by:

y = |x + 3| - 2.

More can be learned about translation concepts at brainly.com/question/4521517

6 0
2 years ago
Read 2 more answers
(X^2-16)/(x^2)-x-12
Mariulka [41]
Answer: (x + 3)(x - 4)

Step-by-Step Solution:

We need to Factorize the given Quadratic Polynomial by using Splitting the Middle Term Method.

= x^2 - x - 12
= x^2 - 4x + 3x - 12
= x(x - 4) + 3(x - 4)
=> (x + 3)(x - 4)
3 0
2 years ago
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