Question

Решите:ctg (3pi/2+arctg7)

Answer 1

Решение
ctg(3π/2 + arctg 7) = - tg(arctg 7) = - 7

Answer 2

To solve the expression, let's break it down step by step.

1. Let's start by simplifying the angle inside the cotangent function: 3π/2 + arctan(7).

2. We know that cotangent is the reciprocal of tangent. So, we can rewrite the expression as the reciprocal of the tangent of the angle: cot(3π/2 + arctan(7)) = 1/tan(3π/2 + arctan(7)).

3. To simplify further, we can use the tangent addition formula: tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a) * tan(b)).

4. In our case, a = 3π/2 and b = arctan(7). Let's substitute these values into the formula: tan(3π/2 + arctan(7)) = (tan(3π/2) + tan(arctan(7))) / (1 - tan(3π/2) * tan(arctan(7))).

5. The tangent of 3π/2 is undefined since the cosine of 3π/2 is 0. Therefore, we can simplify the expression further: 1/tan(3π/2 + arctan(7)) = 1 / (tan(arctan(7))) = 1 / 7.

6. Thus, the solution to the expression ctg(3π/2 + arctan(7)) is 1/7.