Question

the value of cos 15°?​

Answer 1

Answer:

The value of cos 15° = (√3+1)/2√2.

Answer 2

$\\ \footnotesize \quad \bullet \quad \cos (15) = \cos(60 - 45)$

We know that,

$\\ \footnotesize \quad \bullet \quad \underline{\boxed{\rm \cos(A-B) = \cos A. \cos B + \sin A. \sin B}}$

Solution:

$\\ \footnotesize \quad \longrightarrow \quad \cos(60 - 45) = \cos (60). \cos(45) + \sin(60) . \sin(45)$

$\\ \footnotesize \quad \longrightarrow \quad \cos(60 - 45) = \dfrac{1}{2} \times \dfrac{1}{ \sqrt{2} } + \dfrac{ \sqrt{3} }{2} \times \dfrac{1}{ \sqrt{2} }$

$\\ \footnotesize \quad \longrightarrow \quad \cos(60 - 45) = \dfrac{1}{ 2\sqrt{2} } + \dfrac{ \sqrt{3} }{2 \sqrt{2} }$

$\\ \footnotesize \quad \longrightarrow \quad \boxed{ { \cos(60 - 45) = \dfrac{1 + \sqrt{3} }{ 2\sqrt{2} }}}$

$\\ \footnotesize \quad \therefore \quad \boxed{ \pink{ \frak{ \cos(15) = \dfrac{1 + \sqrt{3} }{ 2\sqrt{2} } }}} \bigstar$

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