Question

Упростите пожалуйста
2sin$alpha +$ $frac{2cos^{2} alpha }{1+sin alpha }$

Answer 1

$2 sin alpha + frac{2 cos^2 alpha }{1 + sin alpha } = frac{2 sin alpha (1 + sin alpha) + 2 cos^2 alpha }{1 + sin alpha } = \ = frac{2 sin alpha + 2sin^2 alpha + 2 cos^2 alpha }{1 + sin alpha } = frac{2 sin alpha + 2 (sin^2 alpha + cos^2 alpha) }{1 + sin alpha } = \ = frac{2 sin alpha + 2}{1 + sin alpha } = frac{2( sin alpha + 1)}{1 + sin alpha } = 2.$