Question

[Limited Edition]

Cho \(\tan\alpha=\frac{3}{5}\), hãy tính giá trị của:

a) \(M=\frac{\sin\alpha+\cos\alpha}{\sin\alpha-\cos\alpha}\)

b) \(N=\frac{\sin\alpha\cos\alpha}{\sin^2\alpha-\cos^2\alpha}\)

c) \(P=\frac{\sin^3\alpha+\cos^3\alpha}{2\sin\alpha\cos^2\alpha+\cos\alpha\sin^2\alpha}\)

Answer 1

[Nguyễn Việt Lâm]

\(M=\frac{\frac{sina}{cosa}+\frac{cosa}{cosa}}{\frac{sina}{cosa}-\frac{cosa}{cosa}}=\frac{tana+1}{tana-1}=\frac{\frac{3}{5}+1}{\frac{3}{5}-1}=...\)

\(N=\frac{\frac{sina.cosa}{cos^2a}}{\frac{sin^2a}{cos^2a}-\frac{cos^2a}{cos^2a}}=\frac{tana}{tan^2a-1}=...\) (thay số bấm máy)

\(P=\frac{\frac{sin^3a}{cos^3a}+\frac{cos^3a}{cos^3a}}{\frac{2sina.cos^2a}{cos^3a}+\frac{cosa.sin^2a}{cos^3a}}=\frac{tan^3a+1}{2tana+tan^2a}=...\)