3sin2a-4cos2a/5cos2A-sin2A, если tgA=3

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We know that tgA = 3, which means sinA/cosA = 3. Therefore sinA = 3cosA.

Now we can substitute sinA = 3cosA into the expression:

3sin2a - 4cos2a / 5cos2A - sin2A

= 3(2sinAcosA) - 4(cos^2A) / 5(cos^2A) - sin^2A
= 6sinAcosA - 4cos^2A / 5cos^2A - sin^2A
= 6(3cosA)cosA - 4cos^2A / 5cos^2A - (3cosA)^2
= 18cos^2A - 4cos^2A / 5cos^2A - 9cos^2A
= 14cos^2A / -4cos^2A
= -14

Therefore, the expression 3sin2a-4cos2a/5cos2A-sin2A, when tgA=3, is equal to -14.