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4 votes
Find the exact value of cos 15°

2 Answers

4 votes

Answer:


(√(6) +√(2) )/(4)

Explanation:

User Sumak
by
8.3k points
5 votes

Answer:


(√(6)+√(2) )/(4)

Explanation:

Using the difference formula for cosine and the exact values

cos45° = sin45° =
(√(2) )/(2), cos30° =
(√(3) )/(2), sin30° =
(1)/(2)

cos(a - b) = cosacosb + sinasinb

Note 15° = 45° - 30°, thus

cos15°

= cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= (
(√(2) )/(2) ×
(√(3) )/(2) ) + (
(√(2) )/(2) ×
(1)/(2) )

=
(√(6) )/(4) +
(√(2) )/(4)

=
(√(6)+√(2) )/(4)

User Mlwn
by
7.2k points

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