Question

1- cos 2 x + sin2x *ctgx/1+cos2x+sin2x​

Answer 1

Решение на фотографии

Answer 2

To simplify the expression, let's start by manipulating the terms step by step:

1. Recall the trigonometric identities:

   • cos^2(x) + sin^2(x) = 1
   • cot(x) = 1/tan(x) = cos(x)/sin(x)

2. Substitute these identities into the expression: 1 - cos^2(x) + sin^2(x) * cot(x) / (1 + cos^2(x) + sin^2(x))

3. Simplify further: 1 - cos^2(x) + sin^2(x) * (cos(x) / sin(x)) / (1 + cos^2(x) + sin^2(x))

4. Using the common denominator sin(x), we get: (sin(x) - cos^2(x) * cos(x)) / sin(x) / (1 + cos^2(x) + sin^2(x))

5. Now, use the identity sin^2(x) + cos^2(x) = 1: (sin(x) - cos^3(x)) / sin(x) / 2

6. Finally, simplify the expression by canceling out sin(x) terms: (1 - cos^3(x)) / 2

So, the simplified expression is (1 - cos^3(x)) / 2.