Question

Упростите выражение. (1) Sin альфа ×cos альфа / ctg альфа -1 (2) 1- sin альфа ×cosальфа / #tg альфа

Answer 1

Ответ на картинке... .. .

Answer 2

Simplifying the Expressions

Let's simplify the given expressions step by step:

(1) sin(α) × cos(α) / ctg(α) - 1

To simplify this expression, we can start by simplifying the trigonometric functions:

- The cotangent function (ctg) is the reciprocal of the tangent function (tan). So, ctg(α) is equal to 1 / tan(α). - The product of sine (sin) and cosine (cos) of the same angle α is equal to half the sine of twice the angle. So, sin(α) × cos(α) is equal to 1/2 × sin(2α).

Now, let's substitute these simplifications back into the expression:

sin(α) × cos(α) / ctg(α) - 1 = (1/2) × sin(2α) / (1 / tan(α)) - 1 = (1/2) × sin(2α) × tan(α) - 1

(2) 1 - sin(α) × cos(α) / tan(α)

To simplify this expression, we can again simplify the trigonometric functions:

- The tangent function (tan) is equal to sin(α) / cos(α). So, sin(α) × cos(α) / tan(α) is equal to sin(α) × cos(α) / (sin(α) / cos(α)). - Dividing by a fraction is equivalent to multiplying by its reciprocal. So, sin(α) × cos(α) / (sin(α) / cos(α)) is equal to sin(α) × cos(α) × (cos(α) / sin(α)).

Now, let's substitute these simplifications back into the expression:

1 - sin(α) × cos(α) / tan(α) = 1 - sin(α) × cos(α) × (cos(α) / sin(α))

Simplified Expressions

After simplifying the given expressions, we have:

(1) sin(α) × cos(α) / ctg(α) - 1 = (1/2) × sin(2α) × tan(α) - 1

(2) 1 - sin(α) × cos(α) / tan(α) = 1 - sin(α) × cos(α) × (cos(α) / sin(α))

Please let me know if you need any further clarification or assistance!