Question

Докажите тождество:sin^6(a)+cos^6(a)+3sin^2(a)*cos^2(a)=1Докажите тождество:
sin^6(a)+cos^6(a)+3sin^2(a)*cos^2(a)=1
$sin^6 \alpha +cos^6 \alpha +3sin^2 \alpha cos^2 \alpha =1$

Answer 1

(sin²a)³+(cos²a)³+3sin²acos²a=1
(sin²a+cos²a)³-3(sin²a²)cos²a-3sin²a(cos²a)²+3sin²acos²a=1
1³-3sin²acos²a*(sin²a+cos²a-1)=1
1-3sin²acos²a*(1-1)=1
1-3sin²acos²a**0=1
1-0=1
1=1