Question

sin7a+sin5a\cos5a-cos7a=

Answer 1

sin7a+sin5a /cos5a-cos7a= 2 sin6acosa / -2 sin(-a)sin6a=cosa / sina)= ctga

Answer 2

$\frac{Sin7 \alpha +Sin5 \alpha }{Cos5 \alpha -Cos7 \alpha } = \frac{2Sin \frac{7 \alpha +5 \alpha }{2}Cos \frac{7 \alpha -5 \alpha }{2} }{-2Sin \frac{5 \alpha +7 \alpha }{2}Sin \frac{5 \alpha -7 \alpha }{2} }= \frac{Sin6 \alpha Cos \alpha }{Sin6 \alpha Sin \alpha } =Ctg \alpha$