Изветсно, что tg²a+ctg²a+1/sin²a+1/cos²а=7 вычислить sin²a*cos²a

tg²A+ctg²A+1/sin²A+1/cos²А=7
1/cos²А-1+1/sin²A-1+1/sin²A+1/cos²А=7
2/cos²А+2/sin²A-2=7
1/cos²А+1/sin²A=9/2
(sin²A+cos²А)/cos²А*sin²A=9/2
1/cos²А*sin²A=9/2
cos²А*sin²A=2/9