If =30^ , verify that. 3 =4 ^3 -3 - Vidyadip

Question

If $\theta=30^\circ,$ verify that.
$\cos3\theta=4\cos^3\theta-3\cos\theta$

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Answer

Given:
$\theta=30^\circ\dots(1)$
To verify:
$\cos3\theta=4\cos^3\theta-3\cos\theta\dots(2)$
Now consider left hand side of the expression in equation (2)
Therefore
$\cos3\theta=\cos3\times30$
$=\cos90$
$=0$
Now consider right hand side of the expression to be verified in equation (2)
Therefore,
$4\cos^3\theta-3\cos\theta=4\cos^330-3\cos30$
$=4\bigg(\frac{\sqrt{3}}{2}\bigg)^3-3\times\frac{\sqrt{3}}{2}$
$=\frac{3\sqrt{3}}{2}-\frac{3\sqrt{3}}{2}$
$=0$
Hence it is verified that,
$\cos3\theta=4\cos^3\theta-3\cos\theta$

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