Question

verify that cos=60=1-2sin^2 30=2cos^2 30-1

Answer 1

hope it will help you.

Answer 2

$\cos 60=1-2\sin^{2} 30=2\cos^{2} 30-1=\dfrac{1}{2}$, verified.

Step-by-step explanation:

L.H.S. = $\cos 60$

= $\dfrac{1}{2}$

M.H.S.=$1-2\sin^{2} 30$

$=1-2\times (\dfrac{1}{2} )^{2}$

$=1-2\times \dfrac{1}{4} =1-\dfrac{1}{2}$

$=\dfrac{1}{2}$

R.H.S.$=2\cos^{2} 30-1$

$=2\times (\dfrac{\sqrt{3} }{2} )^{2} -1$

$=2\times \dfrac{3}{4} -1=\dfrac{3}{2} -1$

$=\dfrac{3-2}{2} =\dfrac{1}{2}$

Hence, L.H.S. =M.H.S. = R.H.S.$=\dfrac{1}{2}$

∴ $\cos 60=1-2\sin^{2} 30=2\cos^{2} 30-1=\dfrac{1}{2}$, verified.