Question

Преобразовать сумму в произведение
1 + tg a

Answer 1

$1+tg alpha =1+frac{sin alpha }{cos alpha }=frac{sin alpha +cos alpha }{cos alpha }=frac{sin alpha +sin(frac{pi}{2}- alpha )}{cos alpha }=\\=frac{2sinfrac{pi}{4}cdiot cos( alpha -frac{pi}{4})}{cos alpha }=frac{2cdot frac{sqrt2}{2}cdot cos( alpha -frac{pi}{4})}{cos alpha }=sqrt2cdot cos( alpha -frac{pi}{4})cdot frac{1}{cos alpha }=\\=sqrt2cdot cos( alpha -frac{pi}{4})cdot sec alpha$