Question

[33. Nguyễn Minh Ngọc]

Rút gọn biểu thức: B = sin⁶a + cos⁶a + 3sin²a. cos²a

Answer 1

[Lê Song Phương]

\(B=\sin^6\alpha+\cos^6\alpha+3\sin^2\alpha.\cos^2\alpha\)

\(B=\left(\sin^2\alpha\right)^3+\left(\cos^2\alpha\right)^3+3\sin^2\alpha.\cos^2\alpha\)

\(B=\left(\sin^2\alpha+\cos^2\alpha\right)\left(\sin^4\alpha+\cos^4\alpha-\sin^2\alpha.\cos^2\alpha\right)+3\sin^2\alpha.\cos^2\alpha\)

\(B=\sin^4\alpha+\cos^4\alpha-\sin^2\alpha.\cos^2\alpha+3\sin^2\alpha.\cos^2\alpha\)(vì \(\sin^2\alpha+\cos^2\alpha=1\))

\(B=\left(\sin^2\alpha\right)^2+\left(\cos^2\alpha\right)^2+2.\sin^2\alpha.\cos^2\alpha\)

\(B=\left(\sin^2\alpha+\cos^2\alpha\right)^2=1\)(vì \(\sin^2\alpha+\cos^2\alpha=1\))

Vậy B = 1

Answer 2

[𝚃̷ ❤𝚇̷❤ 𝙷̷]

TL

B=1 nhưng mik ko biết giải thích

K mik nha

Hok tốt