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Пошаговое объяснение:
5(cos^2 x-sin^2 x)-2*2sinxcosx=2(sin^2 x+cos^2 x)
5cos^2 x-5sin^2 x-4sinxcosx-2sin^2 x-2cos^2 x=0
3cos^2 x-7sin^2 x-4sinxcosx=0, делим на cos^2 x не=0
3-7tg^2x-4tgx=0, 7tg^2x+4tgx-3=0, tgx=a, 7a^2+4a-3=0, D=16+84=100,
a1=-4-10/14=-1, a2=-4+10/14=3/7, tgx=-1, x=-п/4+пk, tgx=3/7, x=arctg3/7+пк
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Пошаговое объяснение:
5(cos^2 x-sin^2 x)-2*2sinxcosx=2(sin^2 x+cos^2 x)
5cos^2 x-5sin^2 x-4sinxcosx-2sin^2 x-2cos^2 x=0
3cos^2 x-7sin^2 x-4sinxcosx=0, делим на cos^2 x не=0
3-7tg^2x-4tgx=0, 7tg^2x+4tgx-3=0, tgx=a, 7a^2+4a-3=0, D=16+84=100,
a1=-4-10/14=-1, a2=-4+10/14=3/7, tgx=-1, x=-п/4+пk, tgx=3/7, x=arctg3/7+пк