Đáp án:
Giải thích các bước giải:
`(tan \alpha + cot \alpha)^2=25`
`⇔ \frac{sin^2 \alpha}{cos^2 \alpha}+\frac{cos^2 \alpha}{sin^2 \alpha}+2 . tan \alpha . cot \alpha = 25`
`⇔ \frac{sin^4 \alpha +cos^4 \alpha}{cos^2 \alpha . sin^2 \alpha}=23`
`⇔ sin^4 \alpha + cos^4 \alpha=23 . cos^2 \alpha . sin^2 \alpha`
`⇔ (sin^2 \alpha + cos^2 \alpha)^2=25 . cos^2 \alpha . sin^2 \alpha`
`⇔ 1=25 . cos^2 \alpha . sin^2 \alpha`
`⇔ sin^2 \alpha . cos^2 \alpha=\frac{1}[25}`
`⇔ sin \alpha . cos \alpha = \frac{1}{5}`
`⇔ 2 . sin \alpha . cos \alpha =\frac{2}{5}`
`⇒ sin 2\alpha=2/5`
