Question

( tgα+ctgα ) − 2 при α = −π/4

Answer 1

( tgα+ctgα ) − 2 =( tgα+1/tgα ) − 2= (-1-1)-2=-4

tg(−π/4)=-1

Ответ -4

Answer 2

To find the value of the expression (tgα + ctgα) - 2 when α = -π/4, we first need to determine the values of tangent (tg) and cotangent (ctg) for α = -π/4.

Tangent (tg) and cotangent (ctg) are trigonometric functions defined as follows:

tgα = sinα / cosα ctgα = cosα / sinα

For α = -π/4:

sin(-π/4) = -√2 / 2 cos(-π/4) = √2 / 2

Now, we can calculate the values:

tg(-π/4) = sin(-π/4) / cos(-π/4) = (-√2 / 2) / (√2 / 2) = -1 ctg(-π/4) = cos(-π/4) / sin(-π/4) = (√2 / 2) / (-√2 / 2) = -1

Now, substitute these values into the expression:

(tgα + ctgα) - 2 = (-1 + (-1)) - 2 = -2 - 2 = -4

So, when α = -π/4, the value of (tgα + ctgα) - 2 is -4.