Question

(10) упростите выражение

Answer 1

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