Question

Ctgt*sin(-t)+sin(2pi+t)

Answer 1

Решение
Ctgt*sin(-t)+sin(2pi+t) = (cost/sint)* (- sint) + sint = - cost + sint = 
= √2sin(45° - t)

Answer 2

To simplify the expression Ctgt*sin(-t) + sin(2π + t), let's break it down step by step:

1. Recall that the tangent function is defined as tan(x) = sin(x) / cos(x).

2. Substitute the expression Ctgt with C(sin(t) / cos(t)):

   C(sin(t) / cos(t)) * sin(-t) + sin(2π + t)

3. Next, let's simplify sin(-t) using the trigonometric identity sin(-x) = -sin(x):

   C(sin(t) / cos(t)) * (-sin(t)) + sin(2π + t)

4. Now, distribute C(sin(t) / cos(t)) to both terms:

   -C(sin(t)^2 / cos(t)) + sin(2π + t)

5. Use the trigonometric identity sin(2π + t) = sin(t):

   -C(sin(t)^2 / cos(t)) + sin(t)

6. Finally, you can leave it in this form, or you may want to simplify further depending on the context or specific requirements.

So, the simplified expression is:

-C(sin(t)^2 / cos(t)) + sin(t)