Question

Bài 1: Tính:

a) \(A=4\cos^2\alpha-6\sin^2\alpha\) biết \(\sin\alpha=\frac{1}{5}\)

b) \(B=\sin\alpha.\cos\alpha\) biết \(\tan\alpha+\cot\alpha=3\)

c) \(C=\cot^2\alpha-\cos^2\alpha.\cot^2\alpha\) biết \(\sin\alpha=\frac{3}{4}\)

Answer 1

\(A=4\left(1-sin^2x\right)-6sin^2a=4-10sin^2a=4-10.\left(\frac{1}{5}\right)^2=...\)

\(tana+cota=3\Leftrightarrow\frac{sina}{cosa}+\frac{cosa}{sina}=3\Leftrightarrow\frac{sin^2a+cos^2a}{sina.cosa}=3\)

\(\Leftrightarrow\frac{1}{sina.cosa}=3\Leftrightarrow sina.cosa=\frac{1}{3}\)

\(C=cot^2a-cos^2a.cot^2a=cot^2a\left(1-cos^2a\right)=cot^2a.sin^2a\)

\(=\frac{cos^2a}{sin^2a}.sin^2a=cos^2a=1-sin^2a=1-\left(\frac{3}{4}\right)^2=...\)