Question

If A = ${30}^{\circ }$. Then,

$(\sin A-\cos A{)}^2=1-\sin 2A$
State true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Given: $A={30}^{\circ }$

To Prove: $(\sin A-\cos A{)}^2=1-\sin 2A$
L.H.S: $(\sin A-\cos A{)}^2$

= $(\sin {30}^0-\cos {30}^0{)}^2$

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

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

= $\frac{1+3-2\sqrt{3}}{4}$

= $1-\frac{\sqrt{3}}{2}$
R.H.S: $1-\sin 2A$

= $1-\sin {60}^0$

= $1-\frac{\sqrt{3}}{2}$

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