Question

ПОМОГИТЕ ПОЖАЛУЙСТА ТРИГОНОМЕТРИЯ

Answer 1

$7sin^25x+cos^25x=4sin10x\\\\7sin^25x-4\cdot 2sin5x\cdot cos5x+cos^25x=0\ \Big|:cos^25x\ne 0\\\\7tg^25x-8tg5x+1=0\\\\t=tg5x\ ,\ \ \ 7t^2-8t+1=0\ \ ,\ \ D/4=16-7=9\ \ \to \ \ t_1=\dfrac{1}{7}\ ,\ t_2=1\\\\a)\ \ tg5x=\dfrac{1}{7}\ \ ,\ \ \ 5x=arctg\dfrac{1}{7}+\pi n\ ,\ \ x=\dfrac{1}{5}\, arctg\dfrac{1}{7}+\dfrac{\pi n}{5}\ ,\ n\in Z\\\\b)\ \ tg5x=1\ \ ,\ \ \ 5x=\dfrac{\pi}{4}+\pi k\ ,\ k\in Z\ \ ,\ \ x=\dfrac{\pi}{20}+\dfrac{\pi k}{5}\ ,\ k\in Z$

$Otvet:\ x=\dfrac{1}{5}\, arctg\dfrac{1}{7}+\dfrac{\pi n}{5}\ ,\ x=\dfrac{\pi}{20}+\dfrac{\pi k}{5}\ ,\ \ n,k\in Z\ .$