Question

Tg (a-p)cos (p/2+2)cos (p+a)/sin (-a)ctg (3p/2+a)

Answer 1

$\displaystyle \frac{tg( \alpha - \pi )\cos( \frac{ \pi }{2}+\alpha)\cos( \pi +\alpha) }{\sin(-\alpha)ctg( \frac{3 \pi }{2}+\alpha) } = \frac{tg\alpha(-\sin\alpha)(-\cos\alpha)}{(-\sin \alpha)(-tg\alpha)} =\cos\alpha$

Answer 2

It seems like you've provided a mathematical expression with various trigonometric functions. Let's break down the expression step by step:

Tg (a-p)cos (p/2+2)cos (p+a)/sin (-a)ctg (3p/2+a)

First, let's clarify some trigonometric notation:

• Tg(x) is usually written as tan(x), which represents the tangent function.
• cos(x) represents the cosine function.
• sin(x) represents the sine function.
• ctg(x) is often written as cot(x), which represents the cotangent function.

Now, let's rewrite the expression with these notations:

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

Now, you can simplify this expression further by using trigonometric identities and simplifications:

1. tan(a - p) = -tan(p - a) (Tangent function is odd)
2. sin(-a) = -sin(a) (Sine function is odd)
3. cot(3p/2 + a) = 1/tan(3p/2 + a) (Cotangent function is the reciprocal of the tangent function)

So, the simplified expression becomes:

• tan(p - a) * cos(p/2 + 2) * cos(p + a) / (-sin(a)) * (1/tan(3p/2 + a))

Now, you can further manipulate the expression or compute specific values depending on the values of 'a' and 'p' that you have. If you have specific values for 'a' and 'p', you can substitute them into the expression to obtain a numerical result.