Question

[Joylynn Bun]

Biết 𝐬𝐢𝐧 ∝= 𝟑/𝟓 . Tính : a) 𝐴 = cos ∝ sin3 ∝ + cos3 ∝ sin ∝ b) 𝐵 = cos2 ∝ sin4 ∝ + cos4 ∝ sin2 

Answer 1

[Nguyễn Lê Phước Thịnh]

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

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

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

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

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