Question

Доказать тождество 1/8 - cos^2 a + cos^4 a = 1/8 × cos 4a

Answer 1

$\frac{1}{8} - cos^{2}a+ { \cos}^{4}a= \frac{1}{8} \cos4a$
$\frac{1}{8} - cos^{2}a(1 - { \cos}^{2}a)= \frac{1}{8} \cos4a$
$\frac{1}{8} - cos^{2}a \times sin^{2}a= \frac{1}{8} \cos4a$
$\frac{1}{8} - \frac{1}{4} {sin}^{2} 2a= \frac{1}{8} \cos4a$
$\frac{1}{8} (1 - 2{sin}^{2} 2a) = \frac{1}{8} \cos4a$
$\frac{1}{8} cos4a = \frac{1}{8} \cos4a$