Question

If $a=\sin (100{)}^{\circ }-\sin (10{)}^{\circ }$, then

• A. $a>0$
• B. $a<0$
• C. $a=0$
• D. none of these

Answer 1

The correct option is A $a>0$

$\sin (100{)}^{\circ }-\sin (10{)}^{\circ }$
$=\sin (90+10{)}^{\circ }-\sin (10{)}^{\circ }$
$=\cos (10{)}^{\circ }-\sin (10{)}^{\circ }$

As ${10}^{\circ }\in (0,{45}^{\circ })$, so
$\cos x>\sin x\forall x\in (0,{45}^{\circ })\Rightarrow \cos (10{)}^{\circ }-\sin (10{)}^{\circ }>0\therefore a>0$