Question

Sin3x-sinx cos2x ------------------- Sin3x+sinx

Answer 1

Ну примерно так получается

Answer 2

To simplify the given expression, we can follow these steps:

Step 1: Factor out common terms from the numerator and denominator. Step 2: Use trigonometric identities to simplify the expression.

The expression is:

(sin3x - sinx * cos2x) / (sin3x + sinx)

Step 1: Factor out common terms from the numerator and denominator: In the numerator, we can factor out sinx:

(sin3x - sinx * cos2x) = sinx * (3cosx - cos2x)

In the denominator, we can factor out sinx:

(sin3x + sinx) = sinx * (3cosx + 1)

Step 2: Use trigonometric identities to simplify the expression: Now, we can simplify further by using the identity cos2x = 2cos^2(x) - 1:

(sin3x - sinx * cos2x) = sinx * (3cosx - cos2x) = sinx * (3cosx - (2cos^2(x) - 1)) = sinx * (3cosx - 2cos^2(x) + 1)

(sin3x + sinx) = sinx * (3cosx + 1)

Now, the simplified expression is:

(sin3x - sinx * cos2x) / (sin3x + sinx) = (sinx * (3cosx - 2cos^2(x) + 1)) / (sinx * (3cosx + 1))

Next, we can cancel out the common factor of sinx from the numerator and denominator:

(sin3x - sinx * cos2x) / (sin3x + sinx) = (3cosx - 2cos^2(x) + 1) / (3cosx + 1)

So, the simplified expression is (3cosx - 2cos^2(x) + 1) / (3cosx + 1).