Question

9sin(x)/(sin^3(x)+cos^3(x))

Answer 1

Объяснение:

9sin (x):(sin 13 *x*3*cos(s)^*x)

9sin(x)

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sin(13)*x+3*cos(s)^*x

Answer 2

To simplify the expression 9sin(x)/(sin^3(x) + cos^3(x)), we can start by using trigonometric identities to rewrite the denominator.

Trigonometric identity: sin^3(x) + cos^3(x) = (sin(x) + cos(x))(sin^2(x) - sin(x)cos(x) + cos^2(x))

Now, we know that sin^2(x) + cos^2(x) = 1 (Pythagorean identity), so we can replace it in the denominator:

sin^3(x) + cos^3(x) = (sin(x) + cos(x))(1 - sin(x)cos(x))

Now, the expression becomes:

9sin(x)/[(sin(x) + cos(x))(1 - sin(x)cos(x))]

Next, we can try to simplify it further. Distribute the 9sin(x) to both terms in the denominator:

9sin(x) / [sin(x) - sin^2(x)cos(x) + cos(x) - sin(x)cos^2(x)]

Since sin^2(x) + cos^2(x) = 1, we can replace sin^2(x) with (1 - cos^2(x)):

9sin(x) / [sin(x) - (1 - cos^2(x))cos(x) + cos(x) - sin(x)cos^2(x)]

Simplify further:

9sin(x) / [sin(x) - cos(x) + cos^3(x) + cos(x) - sin(x)cos^2(x)]

Combine like terms:

9sin(x) / [2cos(x) + cos^3(x) - sin(x)cos^2(x)]

And there you have the simplified expression:

9sin(x) / [2cos(x) + cos^3(x) - sin(x)cos^2(x)]