Question

(10) упростите выражение

Answer 1

$frac{cos4a + 1}{ctga - tga} = frac{2cos^{2} 2a - 1 + 1}{ frac{cosa}{sina} - frac{sina}{cosa} } = frac{2 {cos}^{2}2a }{ frac{ {cos}^{2} a - {sin}^{2}a }{sina times cosa} } = frac{2 {cos}^{2}2a}{ frac{ cos2a}{sina times cosa} } = 2cos2a times sina times cosa = 2cos2a times frac{1}{2} sin2a = cos2a times sin2a = frac{1}{2} sin4a$