Question

If A = ${30}^{\circ }$ then

$\sin (A+{30}^{\circ })+\cos (A+{60}^{\circ })=\cos A$
State true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Given, $A={30}^{\circ }$
To Prove, $\sin (A+{30}^0)+\cos (A+{60}^0)=\cos A$
L.H.S: $\sin (A+{30}^0)+\cos (A+{60}^0)$
= $\sin {60}^0+\cos {90}^0$
= $\sin {60}^0$
= $\frac{\sqrt{3}}{2}$
= $\cos {30}^0$
= $\cos A$