103k views
2 votes
Find the exact value of cos15

User DSav
by
7.9k points

2 Answers

1 vote


\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)

User Chrystolin
by
7.9k points
4 votes

Answer:


\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)

User Atheaos
by
7.2k points

Related questions

asked May 19, 2018 197k views
Assad asked May 19, 2018
by Assad
8.1k points
2 answers
0 votes
197k views
asked May 28, 2020 6.0k views
Jamall asked May 28, 2020
by Jamall
8.0k points
1 answer
3 votes
6.0k views