Question

Sin(45-a)/cos(45-a)=1

Answer 1

sin(45° - α)/cos(45° - α) = 1

Найдём ограничения:

cos(45° - α) ≠ 0

45° - α ≠ (π/2) + πn

(π/4) - α ≠ (π/2) + πn

α ≠ - (π/4) + πn , n ∈ Z

sinα/cosα = tgα  ⇒

tg(45° - α) = 1

45° - α = (π/4) + πn

(π/4) - α = (π/4) + πn

α = πn , n ∈ Z

ОТВЕТ: πn , n ∈ Z

Answer 2

A=45+3p/4+pk
Вот ответ

Answer 3

To prove the trigonometric identity sin(45-a)/cos(45-a) = 1, we can use the fundamental trigonometric identity:

tan(x) = sin(x)/cos(x).

In this case, let's substitute x = 45 - a:

tan(45 - a) = sin(45 - a)/cos(45 - a).

Now, we know that tan(45 degrees) = 1 because the tangent of 45 degrees is a well-known trigonometric value. Therefore:

tan(45 - a) = 1.

So, sin(45 - a)/cos(45 - a) = 1, as required.