Question

​4sin45 degrees cos 15degrees=1+square root 3

Answer 1

`\text{R.H.S}\\\\=4\sin 45^(\circ) \cos 15^(\circ) \\\\=4\sin 45^(\circ) \cos (45^(\circ)-30^(\circ))\\ \\=4 \sin 45^(\circ) \left(\cos 45^(\circ) \cos 30^(\circ) +\sin 45^(\circ) \sin 30^(\circ) \right)\\\\=4 \left(\sin 45^(\circ) \cos 45^(\circ) \cos 30^(\circ) +\sin^2 45^(\circ) \sin 30^(\circ) \right)\\`

`=4\left[\frac 1{\sqrt 2} \cdot \frac 1{\sqrt 2} \cdot \frac{\sqrt 3}2 +\left( \frac 1{\sqrt 2} \right)^2 \cdot \frac 12 \right]\\ \\=4\left(\frac{\sqrt 3}4 +\frac 14\right)\\\\=4\cdot \frac 14 \left(1+\sqrt 3\right)\\\\=1+\sqrt 3\\\\=\text{L.H.S}`