Question

$tg^2\alpha(1+cos2\alpha )^2$

Answer 1

Ответ:

$= {sin}^{2} 2 \alpha$

Объяснение:

${tg}^{2} \alpha \times {(1 + cos2 \alpha )}^{2} = {tg}^{2} \alpha \times {(1 + (2 {cos}^{2} \alpha - 1)) }^{2} = {tg}^{2} \alpha \times {(2 {cos}^{2} \alpha )}^{2} = \frac{ {sin}^{2} \alpha }{ {cos}^{2} \alpha} \times 4 {cos}^{4} \alpha = 4 {sin}^{2} \alpha {cos}^{2} \alpha = {(2sin \alpha cos \alpha )}^{2} = {sin}^{2}2a$