Question

Геометрия. Упростить : примеры в закрепе

Answer 1

а) (sin a+1/sin a)²+(cos a+1/cos a)²-tg²a-ctg²a=

sin²a+2+1/sin²a+cos²a+2+1/cos²a-tg²a-ctg²a=sin²a+1/sin²a+cos²a+1/cos²a-tg²a-ctg²a+4=1+1/sin²a+1/cos²a-tg²a-ctg²a+4=1+1/sin²a+tg²a+1-tg²a-ctg²a+4=1+1+ctg²a+tg²a+1-tg²a-ctg²a+4=7

b) cos a(1+cos^-1a+tga)×(1-cos^-1a+tga)=cosa(1+1/cos a +tga)×(1-1/cosa + tg a) =cosa(2 sina/cos a) =

2sin a

c) (1+1/tg²(π/2 + a)×sin²a=1+1/(-ctg²a) × sin²a=1+1/ctg²a×sin²a=1+1/cos²a:sin²a × sin²a=tg²a