Question

$\frac{1-2\left[cos60^{\circ }-cos80^{\circ }\right]}{2sin10^{\circ }}=......$

• A. $2$
• B. $1$
• C. $\frac{1}{2}$
• D. $\frac{3}{2}$

Answer 1

Answer: (B)

We have, $\frac{1-2\left(\cos 60^{\circ }-\cos 80^{\circ }\right)}{2\sin 10^{\circ }}$
$=\frac{1-2\left(\frac{1}{2}-\cos 80^{\circ }\right)}{2\sin 10^{\circ }}$
$=\frac{2\cos 80^{\circ }}{2\sin 10^{\circ }}$
$=\frac{\cos \left(90^{\circ }-10^{\circ }\right)}{\sin 10^{\circ }}$
$=\frac{\sin 10^{\circ }}{\sin 10^{\circ }}=1$