Question

The value of $\frac{\sin 24^{\circ }\cos 6^{\circ }-\sin 6^{\circ }\sin 66^{\circ }}{\sin 21^{\circ }\cos 39^{\circ }-\cos 51^{\circ }\sin 69^{\circ }}$ is

• A. - 1
• B. 1
• C. 2
• D. 0

Answer 1

Answer: (A)

$\frac{\sin 24^{\circ }\cos 6^{\circ }-\sin 6^{\circ }\cos 24^{\circ }}{\sin 21^{\circ }\cos 39^{\circ }-\sin 39^{\circ }\cos 21^{\circ }}=\frac{\sin \left(24^{\circ }-6^{\circ }\right)}{\sin \left(21^{\circ }-39^{\circ }\right)}$
$=\frac{\sin 18^{\circ }}{\sin \left(-18^{\circ }\right)}=-1$