Question

Ctg( п+a)×cos(3п/2 +a)+cos(2п+а)

Answer 1

Tg a * sin a + cos a = sin^2a/cos a + cos a = 1 - cos^2a/cos a + cos a = 1/cos a

Answer 2

Решение задания смотри на фотографии

Answer 3

Let's simplify the given expression step by step:

1. Recall the trigonometric identities:

   • cos(π/2 + a) = sin(a)
   • cos(2π + a) = cos(a)
   • sin(2π + a) = sin(a)
   • cos(3π/2 + a) = -sin(a)

2. Now, substitute the trigonometric identities into the expression:

   Ctg(π + a) × cos(3π/2 + a) + cos(2π + a)

   Since cotangent (ctg) is the reciprocal of tangent (tan), we can rewrite it as:

   1/tan(π + a) × (-sin(a)) + cos(a)

3. Recall that tangent has a periodicity of π, so tan(π + a) = tan(a). Therefore, the expression becomes:

   -1/tan(a) × (-sin(a)) + cos(a)

4. Simplify further:

   sin(a)/tan(a) + cos(a)

5. Use the definition of tangent: tan(a) = sin(a)/cos(a):

   sin(a) / (sin(a) / cos(a)) + cos(a)

6. Now, simplify the expression by multiplying by the reciprocal:

   sin(a) × (cos(a) / sin(a)) + cos(a)

7. The sin(a) term cancels out:

   cos(a) + cos(a)

8. Finally, combine like terms:

   2cos(a)

So, the simplified expression is 2cos(a).