Question

What is cos(75°)cos(15°) =

Answer 1

`\frac 14`

Step by step explanation:

`~~~\cos (75^(\circ)) \cos (15^ \circ)\\\\=\frac 12 \cdot 2 \cos ( 75 ^\circ}) \cos( 15^\circ})\\\\`

`=\frac 12 \left[\cos \left( 75^ \circ + 15^ \circ \right) + \cos \left( 75^(\circ) - 15^(\circ) \right)\right]~~~~~~;[2 \cos a \cos b = \cos( a+b) + \cos(a-b)]\\`

`\\=\frac 12 \left( \cos 90^(\circ) + \cos 60^(\circ) \right)\\\\=\frac 12 \left(0+\frac 12 \right)\\\\=\frac 12 \cdot \frac 12\\\\=\frac 14`