Question

prove that cos square 30 degree minus sin square 30 degree is equal to Cos 60 square degree​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\cos ^{2} 30-\sin ^{2} 30=\cos 60,$ proved.

Step-by-step explanation:

Prove that, $\cos ^{2} 30-\sin ^{2} 30=\cos 60$

L.H.S.=$\cos ^{2} 30-\sin ^{2} 30$

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

[ ∵ $\cos 30=\dfrac{\sqrt{3}}{2} ,\sin 30=\dfrac{1}{2}$]

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

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

$=\dfrac{2}{4}$

$=\dfrac{1}{2}$

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

$=\dfrac{1}{2}$

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