Question

If $\angle A={30}^o$ then show that $\sin A=\sqrt{\frac{1-\cos 2A}{2}}$ if true then enter $1$ and if false then write $0$

Answer 1

Given: $\angle A={30}^o$

To prove:$\sin A=\sqrt{\frac{1-cos2A}{2}}$

L.H.S = $\sin A=\sin 30=\frac{1}{2}$
R.H.S = $\sqrt{\frac{1-cos2A}{2}}=\sqrt{\frac{1-cos2\times 30}{2}}=\sqrt{\frac{1-cos60}{2}}=\sqrt{\frac{1-\frac{1}{2}}{2}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$

Thus, L.H.S = R.H.S

$\sin A=\sqrt{\frac{1-\cos 2A}{2}}$