Question

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  1)    $(1- sin L)(1+sin L) \ sin^{2} L$
  2)    $cos L-cos L * sin^{2} L$
  3)$tg L*ctg L-cos^{2} L$

Answer 1

$frac{(1-sin alpha )(1+sin alpha )}{sin^2 alpha }=frac{1-sin^2 alpha }{sin^2 alpha }=frac{cos^2 alpha }{sin^2 alpha }=ctg^2 alpha \\2); cos alpha -cos alpha cdot sin^2 alpha =cos alpha (1-sin^2 alpha )=cos alpha cdot cos^2 alpha =cos^3 alpha \\3); tg alpha cdot ctg alpha -cos^2 alpha =1-cos^2 alpha =sin^2 alpha$

$tg alpha cdot ctg alpha =frac{sin alpha }{cos alpha }cdot frac{cos alpha }{sin alpha }=1\\sin^2 alpha +cos^2 alpha =1,to 1-sin^2 alpha =cos^2 alpha \\1-cos^2=sin^2 alpha$