1). (1-sint)×(1+sint)/cost 2). 1+ctg²t 3). (1-sin²a)(1+tg²a)=1 3). 1+tg²a+1/Sin²a

1) (1 - sin t)×(1 + sin t ) / cos t = [1 - sin ^ 2 ( t) ] / cos ^ 2 ( t ) = cos ^ (t) / cos ^ 2 (t) = 1,2) 1+ctg²t = 1 + cos ^ 2 ( t ) / sin ^ 2 ( t ) =[ sin ^ 2 (t ) + cos ^ 2 ( t ) ] / sin ^ 2 ( t ) = 1 / sin ^ 2 ( t ) sec ^ 2 ( t ) .3) (1 - sin²a)*(1 + tg²a) = 1.( доказать тождество).[1 - sin ^ 2 a ] * [1 + sin ^ 2 ( a ) /cos ^ 2 ( a )] =[1 - sin ^ 2 ( a ) ] * [ cos ^ 2 ( a ) + sin ^ 2 ( a )] / [cos ^ 2 ( a ) = cos ^ 2 ( a ) * [ 1 / cos ^ 2 ( a ) ] = 1 .4) 1 + tg ² (a) + 1 / sin ² (a) = 1 + sin ^ 2 (a) / cos ^ 2 (a) + 1 / sin ^ (a) =sin ^ 2 (a) * cos ^ 2 (a) + sin ^ 4 (a) + cos ^ 2 (a) ] /sin ^ 2 (a) * cos ^ 2 (a) ={sin ^2(a) * [ 1 - sin ^ 2 (a)] + sin ^ 4 (a) + 1 - sin ^ (a) } / sin ^ 2 (a)* cos ^ (a) =(sin ^ 2 (a) - sin ^ 4 (a) + sin ^ 4 (a) +1 - sin ^ 2 (a) } / sin ^ 2 (a)* cos ^ 2 (a) = 1 / sin ^ 2 (a) * cos ^ 2 (a) = 4 / sin ^ 2 (2a).