Question

ТРИГОНОМЕТРИЯ!!! ПОМОГИТЕ!!! ДАЮ 73 БАЛЛА!!!

Answer 1

405
$frac{sin( alpha + beta )+sin( alpha - beta )}{sin( alpha + beta )-sin( alpha - beta )} = frac{sin alpha cos beta +cos alpha sin beta +sin alpha cos beta -cos alpha sin beta }{sin alpha cos beta +cos alpha sin beta -sin alpha cos beta +cos alpha sin beta } = \ \ =frac{2sin alpha cos beta }{2cos alpha sin beta } = tg alpha ctg beta = frac{tg alpha }{tg beta }$
406
$frac{sin( 45^o+alpha)-cos( 45^o+alpha)}{sin( 45^o+alpha)+cos( 45^o+alpha)} = frac{sin45^ocosalpha+cos45^osin alpha -cos 45^ocosalpha+sin45^osin alpha }{sin45^ocosalpha+cos45^osin alpha +cos 45^ocosalpha-sin45^osin alpha} = \ \ = frac{ frac{ sqrt{2} }{2}(cos alpha +sin alpha -cos alpha +sin alpha)}{frac{ sqrt{2} }{2}(cos alpha +sin alpha +cos alpha -sin alpha )}= frac{2sin alpha }{2cos alpha }=tg alpha$
407
$frac{cos65^ocos40^o+sin65^osin40^o}{sin37^ocos12^o-cos37^osin12^o}= frac{cos(65^o-40^o)}{sin(37^o-12^o)}= frac{cos25^o}{sin25^o}=ctg25^o$
408
cos3αcosα+sin3αsinα=cos(3α-α)=cos2α
409
sin5αcos2α-sin2αcos5α=sin(5α-2α)=sin3α