Question

sin^2x+6cos2x=5sinxcosx помогите решить

Answer 1

$sin^2x+6cos2x=5sinxcosx\\ sin^2x+6(cos^2x-sin^2x)=5sinxcosx\\ sin^2x+6cos^2x-6sin^2x=5sinxcosx\\ 6cos^2x-5sin^2x=5sinxcosx\\ 5sin^2x+5sinxcosx-6cos^2x=0|:cos^2x\neq 0\\ 5tg^2x+5tgx-6=0|\; \; a=tgx\\5a^2-5a-6=0\\D=625=25^2\\a_1=1,5;\; \; a_2=-3\\ tgx_1=1,5\\x_1=arctg1,5+\pi n, n\in Z\\tgx_2=3\\x_2=arctg3+\pi n, n\in Z$