Question

Find:
$\frac{\text{cos}{75}^{\circ }}{\text{sin}{15}^{\circ }}+\frac{\text{sin}{12}^{\circ }}{\text{cos}{78}^{\circ }}-\frac{\text{cos}{18}^{\circ }}{\text{sin}{72}^{\circ }}=$ ______.

• A. 2
• B. 1
• C. - 1
• D. 3

Answer 1

The correct option is B

1

$\frac{\text{cos}{75}^{\circ }}{\text{sin}{15}^{\circ }}+\frac{\text{sin}{12}^{\circ }}{\text{cos}{78}^{\circ }}-\frac{\text{cos}{18}^{\circ }}{\text{sin}{72}^{\circ }}$

$\frac{\text{cos}{75}^{\circ }}{\text{sin}({90}^{\circ }-{75}^{\circ })}+\frac{\text{sin}{12}^{\circ }}{\text{cos}({90}^{\circ }-{12}^{\circ })}-\frac{\text{cos}{18}^{\circ }}{\text{sin}({90}^{\circ }-{18}^{\circ })}$

$=\frac{\text{cos}{75}^{\circ }}{\text{cos}{75}^{\circ }}+\frac{\text{sin}{12}^{\circ }}{\text{sin}{12}^{\circ }}-\frac{\text{cos}{18}^{\circ }}{\text{cos}{18}^{\circ }}(\because \sin ({90}^{\circ }-\theta )=\cos \theta and\cos ({90}^{\circ }-\theta )=\sin \theta )$

$=1+1-1$

$=1$