Question

The value of $\frac{sin{55}^{\circ }-cos{55}^{\circ }}{sin{10}^{\circ }}$ is

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

Answer 1

Answer: (D)

$\sqrt{2}$

$\frac{sin{55}^{\circ }-sin{35}^{\circ }}{sin{10}^{\circ }}=\frac{2cos{45}^{\circ }.sin{10}^{\circ }}{sin{10}^{\circ }}=\sqrt{2}$
$\because sinC-sinD=2cos\frac{C+D}{2}sin\frac{C-D}{2}$