Question

упростите выражение 1/1+ctg2a

Answer 1

Ответь D) sin^2a

1/(1+cos^2a/sin^2a)=1/((sin^2a+cos^2a)/sin^2a)=1/1/sin^2a=sin^2a.

(sin^2a+cos^2a=1)

Answer 2

1/(1+ctg²α)=1/(1+(cosα/sinα)²)=1/(1+cos²α/sin²α)=1/((sin²α+cos²α)/sin²α)=

=sin²α/(sin²α+cos²α)=sin²α/1=sin²α

Otvet: D)sin²α

(ctgα=cosα/sinα, sin²α+cos²α=1)