Question

Упростите выражение.

Answer 1

$cos^2 alpha + frac{sin( frac{ pi }{2}+ alpha )*cos( pi - alpha ) }{ctg( pi - alpha )*tg( frac{3 pi }{2} - alpha )}$     $alpha neq frac{ pi n}{2} ,$  $n$ ∈ $Z$

$cos^2 alpha + frac{sin( frac{ pi }{2}+ alpha )*cos( pi - alpha ) }{ctg( pi - alpha )*tg( frac{3 pi }{2} - alpha )} =cos^2 alpha + frac{cos alpha *(-cos alpha ) }{-ctg alpha *ctgalpha} =$$=cos^2 alpha + frac{cos^2 alpha}{ctg^2 alpha } =cos^2 alpha +cos^2 alpha : frac{cos^2 alpha }{sin^2 alpha } =cos^2 alpha +cos^2 alpha * frac{sin^2 alpha }{cos^2 alpha }=$$=cos^2 alpha +sin^2 alpha =1$