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2 years ago

How do I factor this? cos^4x - sin^4x

Mathematics

2 answers:

padilas [110]2 years ago

6 0

Answer: https://socratic.org/questions/how-do-you-simplify-cos-4x-sin-4x#618537

IgorLugansk [536]2 years ago

4 0

Answer:

Step-by-step explanation:

FYI,

a² - b² = (a + b)(a - b)

f(x) = $cos^{4} x$ - $sin^{4} x$ = (cos²x + sin²x)(cos²x - sin²x) =

= <em>(cos²x + sin²x)(cos x + sin x)(cos x - sin x)</em>

If you need to simplify, then

f(x) = 1 × (cos²x - sin²x) = <em>cos(2x)</em>

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Answer:

The correct option is the first:

∃ an integer d such that 6d is an integer and d ≠ 3

Step-by-step explanation:

If 6d is an integer, then d = 3

Let's divide the statement into two:

Let "If 6d is an integer" be p and "then d = 3" be q.

The statement is a conditional statement. Therefore, we have

p ⇒ q

The negation of p ⇒q, ¬(p ⇒ q) ≡ p ∧ ¬q

I have attached an image proving the above.

Using this: ¬(p ⇒ q) ≡ p ∧ ¬q

Then, we leave p as it is and negate q.

P is "if 6d is an integer"

q is "then d = 3," hence ¬q is "then d ≠ 3."

Therefore, the negation of "If 6d is an integer, then d = 3" is "If 6d is an integer, then d ≠ 3."

The correct option is the first:

∃ an integer d such that 6d is an integer and d ≠ 3

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So, the scale factor of dilation from the larger triangle to the smaller triangle is:

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