Question

Помогите..... Ctg^2t*(-1+1/cos^2t)=????

Answer 1

$ctg^2t*(-1+1/cos^2t)=$$ctg^2t*(-1+1/cos^2t)=-cos^2t/sin^2t+\frac{cos^2t}{sin^2t*cos^2t}= \\ -cos^2t/sin^2t+\frac{1}{sin^2t}=\frac{1-cos^2t}{sin^2t}=\frac{sin^2t}{sin^2t}=1$

(Если cost =/= 0, sint =/= 0,

т.е. при t НЕ равном Pi*n/2  n ∈ Z)