Question

please help me to prove that cos^2A =cos4A.pls pls pls

Answer 1

$cos^{2} a = cos^{2}2a - sin^{2}2a \ frac{1 + cos2a}{2} = 2cos^{2}2a - 1 \ 1 + cos2a = 4cos^{2}2a - 2 \ 4cos^{2}2a - cos2a - 3 = 0 \ D = 1 - 4*4*(-3) = 49 = 7^{2} \ cos2a = frac{1 - 7}{8} = - frac{3}{4} \ or \ cos2a = frac{1+7}{8} = 1$


$2a = ^+_- arccos (-frac{3}{4} ) + 2 pi n$, n ∈ Z ;
$a = ^+_- frac{1}{2} arccos (-frac{3}{4} ) + pi n$, n ∈ Z

2a = 2пk, k ∈ Z
a = пk, k ∈ Z

ответ: $a = ^+_- frac{1}{2} arccos (-frac{3}{4} ) + pi n$, n ∈ Z ; 
            a = пk, k ∈ Z

Answer 2

опять ты

Answer 3

мyдак