Question

Sin t *cos t *ctg t-1=?

Answer 1

Ctg t=cos t/ sin t Sin t* cos t* ctg t-1=(Cos t )^ 2-1 (Cos t)^2-1=0 Cos t1= 1 t= pi*2n Cos t2= -1 t= pi +pi*2n итого ответ : cos t = pi*n

Answer 2

sin t*cos t*ctg t-1 = sin t*cos^2t/sin t -1 = cos^2 t - 1

Answer 3

Calculating the Expression

To calculate the expression sin(t) * cos(t) * ctg(t) - 1, we can use the trigonometric identities for sine, cosine, and cotangent.

First, let's recall the definitions of these trigonometric functions: - Sine (sin): In a right-angled triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. - Cosine (cos): In a right-angled triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. - Cotangent (ctg): The cotangent of an angle is the reciprocal of the tangent of the angle.

Using these definitions and trigonometric identities, we can simplify the given expression.

Trigonometric Identities

The trigonometric identities we will use are: - sin(α) * cos(β) = (1/2) * [sin(α + β) + sin(α - β)] - ctg(α) = 1/tg(α)

Simplifying the Expression

Using the trigonometric identities, we can simplify the expression as follows:

sin(t) * cos(t) * ctg(t) - 1 = (1/2) * [sin(2t) + sin(0)] - 1 = (1/2) * [2 * sin(t) * cos(t)] - 1 = sin(t) * cos(t) - 1

So, the simplified expression is sin(t) * cos(t) - 1.

This is the simplified form of the given expression using trigonometric identities.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.