Question

Cos2a+sin (пи/2+a)cos (пи-a)/ /ctg (пи-a)tg (3пи/2+a) упростить выражение

Answer 1

$\frac{1 - sin^{2} \alpha + cos \alpha×(-cos \alpha ) }{(-ctg \alpha )×(-tg \alpha )} = -sin \alpha$

Answer 2

Simplifying the Trigonometric Expression

To simplify the given expression cos(2a) sin(π/2 + a) cos(π - a) + ctg(π - a) tg(3π/2 + a), we can use trigonometric identities and properties. Let's break it down step by step.

First, we'll simplify the individual trigonometric functions using the provided information from the search results.

1. cos(2a): - From Source we have the following information: cosa = 5/13 and 3π/2 < a < 2π. - We can use the double angle identity for cosine: cos(2a) = 2cos^2(a) - 1.

2. sin(π/2 + a): - From Source we know the trigonometric identity: sin^2(y) + cos^2(y) = 1.

3. cos(π - a): - We can use the difference of angles identity for cosine: cos(π - a) = -cos(a).

4. ctg(π - a) and tg(3π/2 + a): - We'll use the definitions of cotangent and tangent: ctg(π - a) = 1/tan(π - a) and tg(3π/2 + a) = tan(3π/2 + a).

Now, let's simplify each part of the expression using the above information.

Simplified Expression

The simplified expression is as follows: 2cos^2(a) - 1 * sin(π/2 + a) * (-cos(a)) + 1/tan(π - a) * tan(3π/2 + a).

Let's proceed to simplify each part of the expression using the provided trigonometric identities and properties.