Question

Taking A=30 degre verify that cos3A= (4cos³A-3cosA)

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Answer 1

$lhs = \cos(3a)$

$\: \: \: = \cos(90)$

$\: \: \: = 0$

$rhs = 4 { \cos }^{3} a - 3 \cos(a)$

$\: \: \: = 4 { \cos}^{3} 30 - 3 \cos30$

$\: \: \: = 4( \frac{ \sqrt{3} }{2}) {}^{3} - 3( \frac{ \sqrt{3} }{2} )$

$\: \: \: = \frac{3 \sqrt{3} }{2} - \frac{3 \sqrt{3} }{2}$

$\: \: = 0$

$thus \: \: lhs = rhs$