Question

Упростите выражение. Решите примерчик

Answer 1

$(1+cos \alpha )\cdot ctg^2 \alpha \cdot(1-cos \alpha )=(1+cos \alpha )(1-cos \alpha )\cdot ctg^2 \alpha = \\ \\ =(1-cos^2 \alpha )\cdot ctg^2 \alpha =sin^2 \alpha \cdot ctg^2 \alpha =sin^2 \alpha \cdot \frac{cos^2 \alpha }{sin^2 \alpha } = \frac{sin^2\alpha\cdot cos^2 \alpha }{sin^2 \alpha } = \\ \\ =cos^2 \alpha$

Answer 2

(1-cosa)(1+cosa)*ctg²a=(1-cos²a)*ctg²a=sin²a*cos²a/sin²a=cos²a