Question

Taking 2A=60°,find sin 30° and cos 30°,using cos 2A=2cos^2A-1

Answer 1

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Answer 2

$sin(a) = \sqrt{ \frac{1 - cos(2a)}{2} } \\ sin(30) = \sqrt{ \frac{1 - cos(60)}{2} } \\ = \sqrt{ \frac{1 - \frac{1}{ 2} }{2} } = \sqrt{ \frac{1}{4} } = \frac{1}{2}$
$cos(a) = \sqrt{ \frac{1 + cos(2a)}{2} } \\ cos(30) = \sqrt{ \frac{1 + cos(60)}{2} } \\ = \sqrt{ \frac{1 + \frac{1}{ 2} }{2} } = \sqrt{ \frac{3}{4} } = \frac{ \sqrt{3} }{2}$