Question

cos 15=cos(45-30)
$\cos( 15 ) = \cos(45 - 30)$

Answer 1

Answer:

$\red { Value \: of \: cos \:15 }=\green { \frac{\sqrt{3}+1}{2\sqrt{2}}}$

Step-by-step explanation:

$\red { Value \: of \: cos \:15 }\\=cos(45-30)\\=cos\blue {45} cos\: \pink {30}+ sin\blue {45} sin\pink {30}$

$\boxed { \orange {cos(A-B) = cosAcosB + sinAsinB }}$

$= \frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\times \frac{1}{2}$

$= \frac{\sqrt{3}}{2\sqrt{2}}+\frac{1}{2\sqrt{2}}$

$=\frac{\sqrt{3}+1}{2\sqrt{2}}$

Therefore.,

$\red { Value \: of \: cos \:15 }=\green { \frac{\sqrt{3}+1}{2\sqrt{2}}}$

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