Toán Chứng minh sin(a)^6+cos(a)^6=1-3sin(a)^2*cos(a)^2 31/08/2021 By Lyla Chứng minh sin(a)^6+cos(a)^6=1-3sin(a)^2*cos(a)^2
$VT= sin^6a+cos^6a$ $= (sin^2a)^3 + (cos^2a)^3$ $= (sin^2a+cos^2a)(sin^4a-sin^2a.cos^2a+cos^4a)$ $= sin^4a-sin^2a.cos^2a+cos^4x$ $= (sin^2a+cos^2a)^2-2sin^2a.cos^2a-sin^2a.cos^2a$ $= 1-3sin^2a.cos^2a$ $= VP$ (đpcm) Trả lời
Đáp án: Giải thích các bước giải: Ta có: sin$^{6}$a+cos$^{6}$a=(sin$^{2}$a)$^{3}$+(cos$^{2}$a)$^{3}$ =(sin$^{2}$a+cos$^{2}$a)(sin$^{4}$a-sin$^{2}$a.cos$^{2}$a+cos$^{4}$a) =(sin$^{2}$a+cos$^{2}$a)$^{2}$-3sin$^{2}$a.cos$^{2}$a (vì sin$^{2}$a+cos$^{2}$a) =1-3sin$^{2}$a.cos$^{2}$a Trả lời
$VT= sin^6a+cos^6a$
$= (sin^2a)^3 + (cos^2a)^3$
$= (sin^2a+cos^2a)(sin^4a-sin^2a.cos^2a+cos^4a)$
$= sin^4a-sin^2a.cos^2a+cos^4x$
$= (sin^2a+cos^2a)^2-2sin^2a.cos^2a-sin^2a.cos^2a$
$= 1-3sin^2a.cos^2a$
$= VP$ (đpcm)
Đáp án:
Giải thích các bước giải:
Ta có: sin$^{6}$a+cos$^{6}$a=(sin$^{2}$a)$^{3}$+(cos$^{2}$a)$^{3}$
=(sin$^{2}$a+cos$^{2}$a)(sin$^{4}$a-sin$^{2}$a.cos$^{2}$a+cos$^{4}$a)
=(sin$^{2}$a+cos$^{2}$a)$^{2}$-3sin$^{2}$a.cos$^{2}$a (vì sin$^{2}$a+cos$^{2}$a)
=1-3sin$^{2}$a.cos$^{2}$a