Question

Tg(-t)cos t -sin(4p-t)

Answer 1

$tg(-t)Cost-Sin(4\pi-t)=-tgtCost+Sint=-\frac{Sint}{Cost}*Cost+Sint=-Sint+Sint=0$

Answer 2

To simplify the expression Tg(-t)cos t - sin(4π - t), we'll start by breaking it down step by step:

1. Tg(-t) is likely a typo, and I believe you meant Tan(-t), which represents the tangent of the negative angle -t.

2. cos t is the cosine of the angle t.

3. sin(4π - t) can be simplified by using the angle difference identity for sine: sin(α - β) = sin α cos β - cos α sin β. In this case, α = 4π and β = t.

Let's proceed with the simplification:

1. Tan(-t) * cos(t) - sin(4π - t)

2. Using the angle difference identity for sine: sin(4π - t) = sin(4π) * cos(t) - cos(4π) * sin(t) Since sin(4π) = 0 and cos(4π) = 1: sin(4π - t) = 0 * cos(t) - 1 * sin(t) = -sin(t)

Now the expression becomes: Tan(-t) * cos(t) - (-sin(t))

3. Since Tan(-t) = -Tan(t) (tangent is an odd function): -Tan(t) * cos(t) + sin(t)

So, the simplified expression is: -Tan(t) * cos(t) + sin(t).