Question

Help me ? :( no spam or

Answer 1

• tan30=1/√3
• tan60=√3

Now

`\\ \sf\longmapsto tan(\alpha+\beta)=√(3)`

`\\ \sf\longmapsto \alpha+\beta=60\dots(1)`

And

`\\ \sf\longmapsto tan(\alpha-\beta)=(1)/(√(3))`

`\\ \sf\longmapsto \alpha-\beta=30\dots(2)`

Adding both

`\\ \sf\longmapsto 2\alpha=30+60=90`

`\\ \sf\longmapsto sin2\alpha=sin90`

`\\ \sf\longmapsto sin2\alpha=1`