Question

If $A={30}^0$, then

$2{\cos }^{2}A-1=1-2{\sin }^{2}A$

If true enter 1 else 0

Answer 1

$A={30}^{\circ }$
Now, $2{\cos }^{2}A-1=1-2{\sin }^{2}A$
L.H.S: $2co{s}^{2}A-1=2co{s}^{2}30-1$
= $2(\frac{\sqrt{3}}{2}{)}^2-1$
= $2\left(\frac{3}{4}\right)-1$
= $\frac{1}{2}$
R.H.S : $1-2{\sin }^{2}A$
= $1-2{\sin }^{2}30$
= $1-2(\frac{1}{2}{)}^2$
= $1-\frac{1}{2}$
= $\frac{1}{2}$
Thus, $L.H.S=R.H.S$