Question

Find the exact value of cos15

Answer 1

`\cos(15^\circ) = \cos(45^(\circ)-30^(\circ)) = \cos(45^(\circ))\cos(30^(\circ))+\sin(45^(\circ))\sin(30^(\circ)) = \\ \\ =(\sqrt 2)/(2)\cdot (\sqrt 3)/(2)+(\sqrt 2)/(2)\cdot (1)/(2) = (\sqrt 6 +\sqrt 2)/(4)`

Answer 2

`\cos (15)=(√(6)+√(2))/(4)`

Explanation:

We want to find the exact value of

`\cos 15\degree`

We rewrite this expression using compound angles

`\cos (45\degree-30\degree)`

Recall that:

`\cos (A-B)=\cos A\cos B+\sin A\sin B`

We apply this property to obtain:

`\cos (45-30)=\cos 45\cos 30+\sin 45\sin 30`

`\cos (15)=(√(2))/(2) * (√(3))/(2)+(√(2))/(2) * (1)/(2)`

`\cos (15)=(√(6)+√(2))/(4)`