Question

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

Answer 1

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