Question

State true or false.

If A = ${30}^{\circ }$, then $sin({60}^{\circ }+A)-sin({60}^{\circ }-A)=cosA$.

• A. True
• B. False

Answer 1

The correct option is B False

Given, $A={30}^{\circ }$
$\sin ({60}^0+A)-\sin ({60}^0-A)=\cos A$
L.H.S:

$\sin ({60}^0+A)-\sin ({60}^0-A)$

= $\sin ({60}^{\circ }+{30}^{\circ })-\sin ({60}^{\circ }-{30}^{\circ })$

= $\sin \left({90}^{\circ }\right)-\sin \left({30}^{\circ }\right)$

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

= $\frac{1}{2}$
R.H.S: $\cos A=\cos {30}^{\circ }=\frac{\sqrt{3}}{2}$
Thus, $L.H.S.\ne R.H.S$

The given statement is false.