Question

Tgα+ctgα=√8 0<α< Найти: tgα-ctgα

Answer 1

$0$

Answer 2

To find the value of tgα - ctgα, we can use the trigonometric identity:

tgα - ctgα = (tgα * ctgα) / (tgα + ctgα)

Given that tgα + ctgα = √8, we can substitute this value into the equation:

tgα - ctgα = (tgα * ctgα) / √8

To simplify further, we need to express tgα and ctgα in terms of sine and cosine. The identities are as follows:

tgα = sinα / cosα ctgα = cosα / sinα

Substituting these values into the equation, we get:

(tgα * ctgα) / √8 = (sinα / cosα * cosα / sinα) / √8 = 1 / √8 = √2 / 4

Therefore, tgα - ctgα = √2 / 4.