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vikaiobidze
@vikaiobidze
August 2022
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3 sin квадрат x - 4 sin x cos x +5 cos квадрат x = 2
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ShirokovP
Verified answer
3sin^2x - 4sinxcosx + 5cos^2x = 2*1
3sin^2x - 4sinxcosx + 5cos^2x = 2*(sin^2x+cos^2x)
3sin^2x - 4sinxcosx + 5cos^2x = 2sin^2x + 2cos^2x
3sin^2x - 2sin^2x - 4sinx*cosx + 5cos^2x - 2cos^2x = 0
sin^2x - 4sinx*cosx + 3cos^2x = 0 // : cos^2x ≠ 0
tg^2x - 4tgx + 3 = 0
(tgx - 3) (tgx - 1) = 0
tgx = 3
x = arctg(3) + pik, k ∈Z
tgx = 1
x = pi/4 + pik, k ∈Z
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Answers & Comments
Verified answer
3sin^2x - 4sinxcosx + 5cos^2x = 2*13sin^2x - 4sinxcosx + 5cos^2x = 2*(sin^2x+cos^2x)
3sin^2x - 4sinxcosx + 5cos^2x = 2sin^2x + 2cos^2x
3sin^2x - 2sin^2x - 4sinx*cosx + 5cos^2x - 2cos^2x = 0
sin^2x - 4sinx*cosx + 3cos^2x = 0 // : cos^2x ≠ 0
tg^2x - 4tgx + 3 = 0
(tgx - 3) (tgx - 1) = 0
tgx = 3
x = arctg(3) + pik, k ∈Z
tgx = 1
x = pi/4 + pik, k ∈Z