tớ cần câu trả lời

\(a,A=\left(\cos^220^0+\cos^270^0\right)+\left(\cos^240^0+\cos^250^0\right)\\ A=\left(\cos^220^0+\sin^220^0\right)+\left(\cos^240^0+\sin^240^0\right)=1+1=2\\ b,B=\left(\cos^2\alpha\right)^3+\left(\sin^2\alpha\right)^3+3\sin^2\alpha\cdot\cos^2\alpha\cdot\left(\sin^2\alpha+\cos^2\alpha\right)\\ B=\left(\sin^2\alpha+\cos^2\alpha\right)^3=1^3=1\)

\(\cos\alpha=\sqrt{1-\dfrac{9}{25}}=\dfrac{4}{5}\)

a: \(A=\cos\alpha\cdot\sin^3\alpha+\cos^3\alpha\cdot\sin\alpha\)

\(=\dfrac{4}{5}\cdot\dfrac{27}{125}+\dfrac{64}{125}\cdot\dfrac{3}{5}\)

\(=\dfrac{4\cdot27+64\cdot3}{625}\)

\(=\dfrac{300}{625}=\dfrac{12}{25}\)

\(1+\sin^2\alpha+\cos^2\alpha=1+1=2\)

1-sin²α=cos2α

Chọn đáp án D

Ta có:

C = sin 4 α + cos 4 α = sin 4 α + cos 4 α + 2 sin 2 α . cos 2 α - 2 sin 2 α . cos 2 α

= sin 2 α + cos 2 α 2 - 2 sin 2 α . cos 2 α

=  1 - 2 sin 2 α . cos 2 α   ( v ì   sin 2 α + cos 2 α = 1 )

Vậy C =  1 - 2 sin 2 α . c o s 2

Đáp án cần chọn là: A

Ta có: \(A=\left(\sin\alpha+\cos\alpha\right)^2+\left(\sin\alpha-\cos\alpha\right)^2\)

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

=2