Question
If $A = 30^\circ,$ then prove that :$2 \cos^2A - 1 = 1 - 2 \sin^2A$
✓
Answer
Given $A = 30^\circ$
$2 \cos^2 A – 1 = 2 \cos^2 30^\circ – 1$
$=2\left(\frac{3}{4}\right)-1$
$=\frac{3}{2}-1$
$=\frac{1}{2}$
$1-2 \sin ^2 A =1-2 \sin ^2 30^{\circ}$
$=1-2\left(\frac{1}{4}\right)$
$=\frac{1}{2}$
$\therefore 2 \cos ^2 A -1$
$=1-2 \sin ^2 A $
$2 \cos^2 A – 1 = 2 \cos^2 30^\circ – 1$
$=2\left(\frac{3}{4}\right)-1$
$=\frac{3}{2}-1$
$=\frac{1}{2}$
$1-2 \sin ^2 A =1-2 \sin ^2 30^{\circ}$
$=1-2\left(\frac{1}{4}\right)$
$=\frac{1}{2}$
$\therefore 2 \cos ^2 A -1$
$=1-2 \sin ^2 A $
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