Question

Sin ²a + tg (-a)ctg a​

Answer 1

Ответ: -cos^2a. Фото решения прикреплено :)

Answer 2

Let's simplify the expression Sin²(a) + tan(-a)cot(a).

First, we'll work with each term separately:

1. Sin²(a): This is the square of the sine function, which is a trigonometric identity:

   Sin²(a) = 1 - cos²(a)

2. tan(-a): The tangent of the negative angle is the same as the negative tangent of the positive angle:

   tan(-a) = -tan(a)

3. cot(a): The cotangent is the reciprocal of the tangent:

   cot(a) = 1/tan(a)

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

Sin²(a) + tan(-a)cot(a) = (1 - cos²(a)) + (-tan(a))(1/tan(a))

Now, simplify further:

= 1 - cos²(a) - tan(a)/tan(a)

Since tan(a)/tan(a) is equal to 1, the expression becomes:

= 1 - cos²(a) - 1

Now, combine like terms:

= -cos²(a)

So, the simplified expression is -cos²(a).