Question

Câu 4: Cho góc \(\alpha\) thỏa mãn \(\sin \alpha = \frac{3}{5}\). Tính \(P = \sin \left( \alpha + \frac{\pi}{6} \right) \sin \left( \alpha - \frac{\pi}{6} \right)\).

Câu 5: Cho góc \(\alpha\) thỏa mãn \(\sin \alpha = \frac{4}{5}\). Tính \(P = \cos 4\alpha\).

Answer 1

Câu 4:

\(\sin\left(\alpha+\frac{\pi}{6}\right)\cdot\sin\left(\alpha-\frac{\pi}{6}\right)\)

\(=\frac12\cdot\sin\left(\frac{\alpha+\frac{\pi}{6}+\alpha-\frac{\pi}{6}}{2}\right)\cdot cos\left(\frac{\alpha+\frac{\pi}{6}-\alpha+\frac{\pi}{6}}{2}\right)\)

\(=\frac12\cdot\sin\alpha\cdot cos\left(\frac{\pi}{6}\right)=\frac12\cdot\frac{\sqrt3}{2}\cdot\frac35=\frac{3\sqrt3}{20}\)

Câu 5:

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

=>\(cos^2\alpha=1-\left(\frac45\right)^2=1-\frac{16}{25}=\frac{9}{25}\)

\(P=cos4\alpha\)

\(=2\cdot cos^22\alpha-1\)

\(=2\cdot\left(2\cdot cos^2\alpha-1\right)^2-1\)

\(=2\cdot\left(2\cdot\frac{9}{25}-1\right)^2-1=-\frac{527}{625}\)