Question

Cos(p+a) sin(3p/2+a) -ctg(3p/2+a) ctg(p-a)

Answer 1

Ответ:

Пошаговое объяснение:

=--сosa*(-cosa)-(-tga)*(-ctga)=cos^2 a -1= -sin^2a

Answer 2

It seems like you've provided an expression involving trigonometric functions, and you want to simplify it. Let's work through it step by step:

The expression you've given is:

Cos(p+a) * sin(3p/2+a) - cot(3p/2+a) * cot(p-a)

First, let's break this down into individual trigonometric functions and try to simplify each term separately:

1. Cos(p+a) * sin(3p/2+a): We can use the product-to-sum identity for sine and cosine: Cos(p+a) * sin(3p/2+a) = (1/2) * [sin((p+a) + (3p/2+a)) - sin((3p/2+a) - (p+a))]

   Simplify further: = (1/2) * [sin(2p + 2a) - sin(p/2)] = (1/2) * [0 - sin(p/2)] (since sin(2p) = 0) = -(1/2) * sin(p/2)

2. cot(3p/2+a) * cot(p-a): Cotangent is the reciprocal of tangent, so cot(x) = 1/tan(x). We have: cot(3p/2+a) * cot(p-a) = (1/tan(3p/2+a)) * (1/tan(p-a))

Now, simplify each term:

1/tan(3p/2+a) = tan(3p/2+a)^(-1) = -1/tan(3p/2+a)

1/tan(p-a) = tan(p-a)^(-1) = -1/tan(p-a)

So, putting it all together:

cot(3p/2+a) * cot(p-a) = (-1/tan(3p/2+a)) * (-1/tan(p-a)) = tan(3p/2+a) * tan(p-a)

Now, the original expression can be written as:

Cos(p+a) * sin(3p/2+a) - cot(3p/2+a) * cot(p-a) = -(1/2) * sin(p/2) - tan(3p/2+a) * tan(p-a)

That's the simplified form of the expression. If you have specific values for p and a, you can further compute the numerical result.