Question

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

Answer 1

= tgα * (-Sinα) / Sin α * tgα = -1

Answer 2

To simplify the expression, let's break it down step by step:

1. Start with the given expression: Tg (2П+a) * cos (3П/2 - a)/sin (2П+a) * ctg (П/2-a)

2. Rewrite the tangent (Tg) as sine (sin) over cosine (cos): sin (2П+a) / cos (2П+a)

3. Rewrite the cotangent (ctg) as cosine (cos) over sine (sin): cos (П/2-a) / sin (П/2-a)

4. Combine the fractions: (sin (2П+a) * cos (П/2-a)) / (cos (2П+a) * sin (П/2-a))

5. Apply trigonometric identities to simplify the expression further:

   • sin (A - B) = sin A * cos B - cos A * sin B
   • cos (A - B) = cos A * cos B + sin A * sin B

6. Using the above identities, we can rewrite the expression as: (sin 2П * cos a - cos 2П * sin a) / (cos 2П * cos a + sin 2П * sin a)

7. Since sin 2П = 0 and cos 2П = 1, the expression simplifies to: (-sin a) / (cos a) = -tan a

Therefore, the simplified expression is -tan a.