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Luba_88 [7]
3 years ago
13

Simplify (sin^4(x) - cos^4(x)) / (sin^2(x) - cos^2(x))

Mathematics
1 answer:
tekilochka [14]3 years ago
7 0

Answer:

1

Step-by-step explanation:

Using the trig. identity

sin²x + cos²x = 1

Given

\frac{sin^4x-cos^4x}{sin^2x-cos^2x}

sin^{4}x - cos^{4}x ← is a difference of squares and factors as

(sin²x - cos²x)(sin²x + cos²x), then fraction becomes

= \frac{(sin^2x-cos^2x)(sin^2x+cos^2x)}{sin^2x-cos^2x} ← cancel (sin²x - cos²x) on numerator/ denominator

= sin²x + cos²x

= 1

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Answer: the arithmetic sequence is

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Step-by-step explanation:

In an arithmetic sequence, the consecutive terms differ by a common difference. This means that the difference between the first term and the second term must equal the difference between the second term and the third term.

Considering the following sequences,

1) 4 - 1 = 3

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