Question

Sin(90-a)+cos(180+a)+tg(270+a)+ctg(360+a)

Answer 1

Ответ: Нуль.

Пошаговое объяснение: используя формулы приведения, получим

sin(90-α)+cos(180+α)+tg(270+α)+ctg(360+α)=cosα-cosα-ctgα+ctgα=0

Answer 2

To simplify the given expression, we'll use trigonometric identities. Here's how we can do it step by step:

1. Recall some fundamental trigonometric identities:
   • sin(90 - θ) = cos(θ)
   • cos(180 + θ) = -cos(θ)
   • tan(270 + θ) = -cot(θ) or cot(-θ)
   • cot(360 + θ) = cot(θ)

Now let's apply these identities to simplify the expression:

sin(90 - a) + cos(180 + a) + tan(270 + a) + cot(360 + a)

= cos(a) + (-cos(a)) + (-cot(a)) + cot(a)

= cos(a) - cos(a) - cot(a) + cot(a)

The two middle terms cancel out:

= 0

So, the simplified expression is 0.