Question

Sa se simplifice fractia sin 7x- sin 5x / cos 7x - cos 5x

Answer 1

Aplicam formulele de transformare a sumelor in produse:
sina-sinb=2sin[(a-b)/2]*cos[(a+b)/2] si cealalta cosa-cosb=-2sin[(a+b)/2]sin[(a-b)/2]
$\frac{sin7x-sin5x}{cos7x-cos5x}= \frac{2sinx*cos6x}{-2sin6x*sinx}=- \frac{cos6x}{sin6x}=ctg6x$