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What is the exact value of

What is the exact value of-example-1
User Gabi Kliot
by
7.9k points

2 Answers

7 votes

Answer:

4th option

Explanation:

using the addition formula for cosine

cos(a - b) = cosacosb + sinasinb

note that 15° = (45 - 30)° , then

cos15°

= cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

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

=
(√(6) )/(4) +
(√(2) )/(4)

=
(√(6)+√(2) )/(4)

=
(√(2)+√(6) )/(4)

User MIPB
by
8.5k points
8 votes

Answer:


\cos 15^(\circ)= (√(2)+√(6))/(4)

Explanation:

Trig Identity:


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


\begin{aligned}\implies \cos 15^(\circ)=\cos (45^(\circ)-30^(\circ)) & =\cos 45^(\circ) \cos 30^(\circ) + \sin 45^(\circ) \sin 30^(\circ)\\\\& = (√(2))/(2) \cdot (√(3))/(2) + (√(2))/(2) \cdot (1)/(2)\\\\& = (√(2)√(3))/(2 \cdot 2)+(√(2) \cdot 1)/(2 \cdot 2)\\\\& = (√(2\cdot 3))/(4)+(√(2))/(4)\\\\& = (√(6)+√(2))/(4)\\\\& = (√(2)+√(6))/(4)\end{aligned}

User Anishsane
by
8.2k points

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