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30 tháng 10 2021

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

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

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

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

TL

B=1 nhưng mik ko biết giải thích

K mik nha

Hok tốt

29 tháng 8 2018

a, A = 2

b, B = 1

\(A=\left(sin^2a+cos^2a\right)^3-3\cdot sin^2a\cdot cos^2a\left(sin^2a+cos^2a\right)+3\cdot sin^2a\cdot cos^2a\)

\(=1-3\cdot sin^2a\cdot cos^2a+3\cdot sin^2a\cdot cos^2a\)

=1

b: \(=\left(\cos^2\alpha+\sin^2\alpha\right)^3-3\cos^2\alpha\sin^2\alpha\left(\sin^2\alpha+\cos^2\alpha\right)+3\cdot\sin^2\alpha\cdot\cos^2\alpha\)

=1

NV
5 tháng 12 2021

\(cos^4a-sin^4a+1=\left(cos^2a-sin^2a\right)\left(cos^2a+sin^2a\right)+1\)

\(=cos^2a-sin^2a+1=cos^2a-sin^2a+sin^2a+cos^2a\)

\(=2cos^2a\)

\(cos^6a+sin^6a+3sin^2a.cos^2a\)

\(=\left(cos^2a+sin^2a\right)^3-3sin^2a.cos^2a\left(sin^2a+cos^2a\right)+3sin^2a.cos^2a\)

\(=1-3sin^2a.cos^2a.1+3sin^2a.cos^2a\)

\(=1\)

8 tháng 8 2021

$\sin^4 a-cos^4 a+2\sin^2 a.\cos^2 a\\=(\sin^4 a-\cos^4 a)+2\sin^2 a.\cos^2 a\\=(\sin^2 a+\cos^2 a)(\sin^2-\cos ^2 )+2\sin^2 a.\cos^2 a\\=\sin^2 a-\cos^2 a+2\sin^2 a.\cos^2 a$

3 tháng 7 2021

\(\left(1+tan^2a\right)\left(1-sin^2a\right)-\left(1+cot^2a\right)\left(1-cos^2a\right)\)

\(=\left(1+\dfrac{sin^2a}{cos^2a}\right).cos^2a-\left(1+\dfrac{cos^2a}{sin^2a}\right).sin^2a\)

\(=cos^2a+sin^2a-sin^2a-cos^2a=\)\(0\)

Vậy B=0

NV
4 tháng 6 2020

\(\frac{cos7a+cos3x-2cos5a}{sin6x-sin4a}=2m\Leftrightarrow\frac{2cos5a.cos2a-2cos5a}{2cos5a.sina}=2m\)

\(\Leftrightarrow\frac{2cos5a\left(cos2a-1\right)}{2cos5a.sina}=2m\Leftrightarrow\frac{cos2a-1}{sina}=2m\)

\(\Leftrightarrow\frac{-2sin^2a}{sina}=2m\Leftrightarrow sina=-m\)

\(\Rightarrow cos2a=1-2sin^2a=1-2m^2\)