(sina+1/sina)^2+(cosa+1/cosa)^2-tg^2a-ctg^2a

(sina+1/sina)²+(cosa+1/cosa)²-tg²a-ctg²a=sin²a+2sina*1/sina+1/sin²a+cos²a+2cosa*1/cosa+1/cos²a-sin²a/cos²a-cos²a/sin²a=(sin²a+cos²a)+2+2+1/sin²a+1/cos²a-sin²a/cos²a-cos²a/sin²a=5+(1-sin²a)/cos²a+(1-cos²a)/sin²a=5+(cos²a/cos²a)+(sin²a/sin²a)=5+1+1=7